Determine what level of literacy the character has, and try to imagine what his writing style is probably like. Look to the canon (the original book, movie or play) to see if there are any hints about his upbringing and education that would tell you what sort of literary education he has. Alternately, imagine the autobiography as being spoken or dictated, rather than written; this is a good option if the character is illiterate or has a low literacy level.
Examine the canon and look at the character's dialogue. Decide if the character is likely to write in the same way she talks; if she is introverted and shy, you may decide to make her writing style more verbose, but if she's extroverted, her writing voice should probably be more like her speaking voice. Look for distinctive idiosyncrocies like slang or use of metaphor. There aren't right or wrong answers, but the more you can take distinctive characteristics from the text, the better.
Do some preliminary writing exercises to help you determine the character's voice. Write quick retellings of popular stories, like fairy tales, as they would be told in the voice of the character.
Write a summary of the character's life yourself. Start with all the details and clues you can find in the canon, then fill in the blanks with your own created events. Make this summary detailed; the more events you include, the richer you'll be able to make the autobiography, even if all the details don't make it into the final draft.
Look at the summary and ask yourself about the character's biases regarding the story's events. Decide which of the life events are probably the most important in the character's mind; the most important things should be told in detail and through anecdotes, while the less important details should merely be summarized. Decide whether the character is likely to omit certain details or even lie about them.
Write a short set of notes about each of the most important people in the character's life. Summarize how the character feels and thinks about each of these people.
Draft the autobiography in the mindset of the character. Spend a little time before each writing session trying to imagine that you are the character. Think about how you feel about the process of writing and what sort of setting you're writing in. Imagine the emotions that come up as you write about events and how that will affect the telling of the tale.