Adult DNA cloning: (aka cell nuclear replacement) This technique produces a duplicate of an existing animal. It has been used to clone a sheep,  and other mammals. The DNA from an embryo is removed and replaced with the DNA from an adult animal. Then, the embryo is implanted in a womb and allowed to develop into a new animal. It has not been tried on humans. It has the potential of producing a twin of an existing person. (U.S. Firm Clones Human Embryo for Cells)  

Every cell in the body contains the genetic code to theoretically create an exact clone of the original body- except the sperm and egg. Our cells have been  programmed to perform limited functions.  The other functions are either dormant or turned off. Most scientists had believed that such differentiated cells could not be reprogrammed to be capable of behaving in the same fashion as as a fertilized egg.  In the case of the sheep "Dolly"  a cell was taken from the mammary tissue of a mature 6 year old sheep while its DNA was in a dormant state. It was fused with a sheep ovum with the  nucleus removed. The cell was stimulated with an electric pulse. Out of 277 attempts at cell fusion, 29 began to divide. These were implanted in ewes. 13 became pregnant and one lamb- Dolly, was born.

Similar experiments on other species such as mice were  unsuccessful. There is debate as to why.

Scientists wondered whether Dolly would be fertile, such as in the case of cross species breeding which produces invariably infertile mules. As well some cloned frogs are also infertile.