Winding the coils from wire stock
The wire is fed directly off a large coil (below), handled via a drilled wooden block, and twisted around the appropriate mandrel.  Hand turning is slow and physically tiring but is the safest way to learn.  Drill winding is much faster but the risks of producing a poor quality coil go up.
The mandrels I use have forked ends, so the coil can be slid off without awkward cutting.
The wire is fed in through a hole in this block of wood, at right.  This allows a constant and controllable backward 'pull' on the wire and can also be pressed into the coil as it forms.  This close-in pressing stops the wire looping over itself or the coil helix opening up.
Next Step:  Cutting the coil into looselinks