Judging from
- my own experience (met Nicki at a German con two years ago),
- reports about her recent convention appearances,
- and the content and style of her blog
Nicki is really cool with the fan aspect of her life and enjoys most of the attention, I guess. Hence, I'm sure he'd be happy to read your letter and send you an autograph.
Well, like Lex I have never written genuine fan mail, but like Lex I don't shy away from giving advice anyway.

Actually, a similar question was asked over at the
Luciana Carro Fan Board, and here's a modified version of what I came up with back then:
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As for the content in general, Lex emphasized the need for keeping it decent and normal already.
Regarding the specific, personal content, however, there are necessarily huge differences between one fan and another, depending on how you became a fan, which of her productions you saw, which of her interviews you read, which interests or traits you share, and what kind of connection you may feel.
It certainly need not be a whole essay or something like that. A succinct letter might do the trick as well (that is, convey your feelings of general and particular appreciation for whatever is relevant in your case, and maybe even include some polite questions).
I understand that we are rarely asked or supposed to express appreciation for (or acknowledge inspiration by) a particular person in such a compact manner in real life. Let alone for a person who lives so far away. On top of that, one may feel uneasy because of the alleged "immaturity" of being a fan (read Solium's
essay to quell these infidel thoughts

).
Once we're eventually writing fan mail, all of this may result in an unusually emphatic and/or introspective style which we are simply not accustomed to. That's
not necessarily bad, though. Well, hope this helps a little bit.
Disclaimer: I'm just guessing, so don't blame me if you're getting a restraining order in return.