The film defies logical explanation. It focuses on the stories-cum-life strands of six singers lives. The singers lives bear a similarity to Dylan or the stories he's told about himself.
The stories themselves aren't linear (i.e we don't finish one story before moving on to the next), so at any one time, you've got three stories going on and the film jumps between them. To reduce confusion, however, we do start with the 3 younger 'Dylans,' and loose the younger ones as the film progresses (only to have them replaced with older 'Dylans' later on in the film).
Reading this, you might think that it's a mess of a film, but it isn't, even if it doesn't explain some of these Dylan clones actions (like going 'electric' for example).
It's a good film and I would have nominated Blanchett for the Best Actress oscar for this film, rather than for Elizabeth.