As it's a fan project, there's a question that needs to be asked:
Is it a project that either allows for or encourages OC's (Original Characters, i.e. Warhammer, Elder Scrolls etc), or is it one where there's little to no scope for that, and as such you are writing from the POV of the characters from whatever it is you're fanning over?
If the former, and you plan on using Original Characters, you first need to build them from the bottom up. Get a good idea of what they look like, how they act, what their quirks are, what their flaws are, why they hate parakeets that much etc. Another thing you'll want to avoid, espiecially with OC's, is Mary Sue Syndrome, wherein the character is basically "I am like unto a god, fear meh!" make sure that the combat/romance/whatever difficulty curve is believable. Throwing a combat monstrosity cyborg into a setting where they've only just got fire sorted is Mary Sue. Taking that same combat monster and putting them into a setting where such monstrosities are commonplace, some as powerful, some more, some less, but giving your character that one little quirk that gives them a believably decent victory rate is not. The same can be applied to romantic stories, dropping a good-looking girl into an all boys school means that she pretty much has the pick of the ones that aren't gay, that same girl in a mixed school has to sit back and think about what she wants/needs and how she is going to get it.
If it's not an OC-friendly setting, then the characters need to be developed from the top down. Go back over the series/game/whatever and watch the characters, how they interact differently with different characters, what are their speech patterns, what are their behavioural quirks, their history, why they need to drop f-bombs every third word etc, and take notes. It may be a bit tedious, but unless you understand the characters you love so much, you risk making them look bad, which you (mostly) don't want.
When you sit down to actually do the writing, let it flow, don't force it, take breaks, refer to any notes that you make have made in the run up to your writing session. Don't be afraid to delete whole pages of content if it's not working the way you want it to do.
As far as I'm concerned, fan projects are a good way to actually get into writing, especially with the character development side of things.
If it helps, put on some instrumental music. The lack of voice in the the music will give you some relaxation and inspiration without putting words into your mouth.
hope this helped, happy writing