PANU ANSWERS:
The difference between generally subordinated clauses, direct relative clauses and indirect relative clauses is a difficult one for English-speakers.
Mike's three examples mean, respectively, I believe that...is...; The man that is...; The man whose son is..." I hope that the difference, in English, between the first one and the two others is clear, at least. The first one is a generally subordinate clause, which means that the fact or meaning stated in the subordinate clause is subordinate to the verb in the main clause. The subordinate clause in its entirety is the object of the verb in the main clause. Let's look at a whole sentence:
Creidim go bhfuil an ríomhaire seo ar ainghléas. "I believe that this computer is out of order."
Well, what do I believe? I believe the fact, or the entire statement, that this computer is out of order. I believe the whole subordinate clause. So, that's why I have there a go/nach clause: the believing is about the meaning of the entire clause.
Then, the second example. I think I will make it a whole sentence:
Tchí mé an fear atá ag múineadh eolaíocht i mBunscoil an Iúir. "I see the man who is teaching science at the Irish-language elementary school in Newry." (For those of you who never got past the Caighdeán, tchí mé means the same as feicim - or feiceann mé, for that matter.)
Who or what do I see? I see the man. I do not see the fact that is described in the subordinate clause - the subordinate clause is there only to provide information about the man, who is now the only linkage - we call it the correlate of the relative clause - between the verb of the main clause (which tells that I see him) and the subordinate clause (which provides the additional information). Compare:
Tchí mé go bhfuil an fear ag múineadh eolaíocht i mBunscoil an Iúir. "I see that the man is teaching science at the Irish-language elementary school in Newry". Here, I see the whole fact of his teaching science there.
I hope this is enough to make the difference between relative and generally subordinate clause intelligible. However, as we will see below, it will become more complicated wehen we come to the indirect relative clause.
We saw that a relative clause points at one noun or at one pronoun in the main clause, called the correlate of the relative clause. Now, in Irish there exists a substantial difference between the relative clause whose correlate is written out only in the main clause - the direct relative clause - and the relative clause whose correlate is written out in the relative clause, too - the indirect relative clause.
The direct relative clause is signified by the particle a, which lenites (aspirates) the initial consonant of the verb. In Connacht and Ulster Irish, the verb, if it is in present or future tense, also takes on a suffixed broad -s, but this is not the case in Munster, where the verb keeps its original ending. The -idh of the future tense gives way to the -s: glanfaidh "will clean" -> a ghlanfas; ceilfidh "will conceal" -> a cheilfeas; fosclóchaidh/foscólfaidh "will open" -> a fhosclóchas/a fhoscólfas. The -ann of the present tense used to drop away before the -s too, but as this makes the difference between future and present very hard to hear with many verbs, forms such as a ghlananns, a cheileanns, and a fhosclaíonns are quite plausible and cannot be dismissed (for snobs, of course, the historically more correct forms a ghlanas, a cheileas, a fhosclaíos may suggest themselves). In the present tense, the irregular verbs "to be" and "to say" have irregular forms without either lenition or -s: atá (but a bhío[nn]s in the habitual present; a bíos for a bhío[nn]s is confined to Ulster Irish) and adeir or a deir; in both cases, the unleniting a- is a survival of an earlier a- belonging to the stem, reinforced by the relative a. (Now, a deireanns, as well as deireann in the main clause, are quite common, but atá does not usually take the -s; the existence of a lenited a thá in the Munster vernacular is seldom shown in the written language.)
Now, the question is: WHEN DO YOU USE DIRECT RELATIVE CLAUSES? Well, the basic rule is: when the correlate is not written out in the subordinate clause. That means, above all, when it is the subject of the subordinate clause; or, when it is the object of it. In the second case, however, even the indirect clause is possible, but then the object has to be written out; if it is not written out, then a direct relative clause is required. "Writing out" means that the relative clause contains a pronoun, a prepositional pronoun, or a possessive adjective, which refers to the correlate.
If we have a straightforward subject as a correlate: "I saw the man who is teaching science at Bunscoil an Iúir", then there should be no problem: "the man", which is - incidentally - the object of the main clause - I saw the man - is the subject of the subordinate clause: the man is teaching science at Bunscoil an Iúir. (Remember that it is the subordinate clause itself, and the position of the word in it, that settles the matter.) Now, look at this: Chonaic mé an fear atá ag múineadh eolaíocht i mBunscoil an Iúir. Well, who did I see? The man...who is defined by the whole relative clause: who is teaching science at Bunscoil an Iúir. And he is the subject of the relative sentence: he is teaching.
Remember that it is only the position of the correlate in the relative clause that matters. It could also be the subject of the main clause, or it could only be referred to with a prepositional phrase in the main clause:
Tá aithne agam ar an fhear atá ag múineadh eolaíocht i mBunscoil an Iúir."I know the man who is..."
An fear atá ag múineadh eolaíocht i mBunscoil an Iúir, is cara liom é. "The man who is..., he is a friend of mine."
Now, what are the other cases when we have a direct relative clause? Primarily, when the correlate is the object of the relative clause: Cailleadh an tArd-Dhiúc Ferdinand leis an philéar a scaoil Gavrilo Princip. "The Archduke Ferdinand was killed by the bullet that Gavrilo Princip shot." (In English, it would probably be more natural to say ...that was shot by G.P., but we'll prefer the other way in Irish.) It would also be possible to write here an indirect relative clause: ...ar scaoil G.P. é, if we write out the é referring to the bullet (an piléar), but in this case the direct relative is preferred; however, if the sentence is ambiguous, indirect relative can be used if the correlate is the object of the sentence.
It is also possible that the correlate is not a real object, but a word for a unit of time used without preposition and thus behaving like an object. Look at this simple sentence: Chonaic mé an cailín deas sin an chéad uair riamh an oíche udaí Tigh Mhic Pháidín. "I saw that nice girl for the first time ever at McFadden's." In Irish, we don't say "for the first time ever" but "the first time ever", an chéad uair riamh, and although the sentence already has an object an cailín deas sin, the phrase an chéad uair riamh also is a kind of an object as it does not have a preposition and as it clearly isn't the subject. The same applies even better to the phrase an oíche udaí, "that (yon) night".
Now, if we find it necessary to have this kind of words for time as correlates, they behave mostly like an object:
Bhí mé ag déanamh mo mharana ar an oíche a chonaic mé an cailín deas sin an chéad uair riamh tigh Mhic Pháidín. "I was thinking of the night I saw that nice girl for the first time ever at McFadden's."
However, you should remember that it is notoriously difficult to give any definite rules about whether time-determiners of this kind should be followed by direct or indirect clauses. Both seem to have wide currency in written and spoken language. You should really try to read lots of literature and develop some kind of Sprachgefühl or instinct for it. "An oíche a bhfaca mé..." would probably not be wrong, although I myself prefer the other alternative.
Funnily enough, the negative form of the direct relative clause begins with a nach or nár, and has the dependent form of the verb - the verb and the verbal particle are the same as with a generally subordinate clause or an indirect relative clause. So, if we do say an fear a chuaigh go Baile Átha Cliath, "the man who went to Dublin", we also say an fear nach dteachaigh go Baile Átha Cliath "the man who did not go to Dublin" - cf. the generally subordinate clause
[chuala mé] nach dteachaigh sé go Baile Átha Cliath "I heard he did not go to Dublin"
and the indirect relative
[is fear é] nach dteachaigh scian an mháinlia riamh air "[he is a man] whom the knife of the surgeon has never touched" (i.e. who never has been in any need of a surgeon's treatment).
The corresponding affirmative clauses all look different:
[an fear] a chuaigh go BÁC (direct relative)
[chuala mé] go dteachaigh sé go BÁC (generally subordinate clause)
[is fear é] a dteachaigh scian an mháinlia go minic air (indirect relative)
The Indirect Relative Clause probably was formally the same as the "go/nach" clause in the beginning. Typically, in Munster Irish, the indirect clauses still begin with a go/gur, instead of the eclipsing a (or, in the past tense, the aspirating ar) of the standard. Thus, in Munster we say:
chuala go gcuaigh/gur chuaigh sé go Baile Átha Cliath (generally subordinate)
AND:
is fear é gur chuaigh/go gcuaigh scian an mháinlia go minic air (indirect relative)
(In Munster, they really say go gcuaigh, gur chuaigh instead of go dteachaigh as in Ulster or go ndeachaighas in the Caighdeán Oifigiúil - they also frequently use go instead of gur these days - this just as an explanation, if somebody wonders why I didn't write chuala mé go dteachaigh... or is fear é go dteachaigh...air.)
However, in most other dialects, the indirect relative clause is initiated with an a and the dependent form of the verb, which is eclipsed, except the past tense forms of regular verbs, which are preceded by an aspirating ar. The example above is thus written in Ulster Irish as
is fear é a dteachaidh scian an mháinlia go minic air.
When is a relative clause indirect? Well, the main rule is: when you write out the correlate in the subordinate clause itself. The relative clause ...a dteachaidh scian an mháinlia go minic air includes the prepositional pronoun air, which refers to the correlate fear. So, the wird-for-word translation for the whole thing is
he is a man that the knife of the surgeon went often on him.
In English, we say something like "...that the knife of the surgeon went often on" - i.e. not "on him". But in Irish, the air means actually "on him" - it includes both the preposition and the pronoun - and if we have there a woman, then the prepostional pronoun agrees with it:
Is bean í a dteachaidh...uirthi.
It even agrees with other persons:
Is mise Fionn Mac Cumhaill a gcuala sibh trácht go minic orm. "I am F. Mac C. whom you have heard so much mentioned about" - or, word-for-word: "...that you heard so much mention on me".
It is really like this - you should note it!
What makes a relative clause indirect, is historically speaking the word found inside the relative clause which stands fpr the correlate and is written out. The written-out element is most often a prepositional pronoun, but it can also be a possessive adjective:
Chonaic mé an fear a bhfuil tú len nighin a phósadh. "I saw the man whose daughter you are going to marry". Please note that the written-out element is the possessive adjective "his" ("the man that you are going to marry his daughter"), which answers the question "whose?".
Look also at these two sentences:
Sin é an bád a bhfuil Pádraig á stiúradh.
Sin é an bád atá Pádraig a stiúradh
The two sentences mean the same("that is the boat that Patrick is steering"), but in the first one the relative clause is indirect, in the second case it is direct. What sense does this make?
Well, you should remember that the combination dá/dhá/á is actually composed of two elements, do = "to" and a = his, her, its, their (in this particular case, the initial consonant does not mutate). In the first one, we have them both there - including the "a" which means "its". In the other one, there is only the "a" (reduced "do") which means "to". So, there is no written-out pronoun or anything referring to the correlate, and consequently the relative clause is direct.
Remember that regular verbs take the leniting ar in past tense, instead of the eclipsing a of other tenses. (However, in Munster, as we saw, the -r is dying out these days. If you happen to read Maidhc Dainín Ó Sé, keep this in mind.)
Look at this:
Sin é an fear ar thagair mé dó = That is the man I meant("referred to"). (If you would say "...the man I [usually] refer to", that would be ...an fear a dtagraím dó.)
Of course, the autonomous verb of the past tense resists lenition, at least with regular verbs:
Sin é an fear ar tagraíodh dó. = That is the man that people referred to.
(However, it is worth noting that in the smallest Irish-speaking area, Ring of Waterford, the autonomous verb of the past tense is actually lenited, as it is in Scots Gaelic. But this is not supposed to be imitated by learners, with the possible exception of learners living in frequent contact with speakers of this dialect.)
And, of course, remember that irregulat verbs are...well, irregular:
Sin é an fear a gcuala muid an oiread sin iomrá air. = That is the man we have heard so much about. (Of course, Sin é an fear ar chuala muid an oiread sin iomrá air is also possible.)
Regrettably, there is a kind of "relative clause" which simply does not fit into this scheme: it is introduced by the very same eclipsing a or aspirating ar as the indirect relative, and if there is a meaningful difference between absolute and dependent verb forms (such as tá vs. fuil, gheibh vs. faigheann, gheobhaidh vs. faighfidh, déarfaidh vs. abórfaidh), the dependent form is, of course, used in this kind of clauses. But it is very possible indeed that a clause of this kind be "directly relative" in the sense that the correlate is the subject or the object of the relative clause, and not written out. Look at this:
Tá aithne agam ar a rabh i láthair ansin. = I know all (the people) that were present there. - Here the subject of the relative clause is the a = "all (who)", and it is not written out in the relative clause itself, so in principle this should be a kind of direct relative.