First thing is to take it slow. There are lots of rules. You're not going to memorize them immediately, so don't make that a goal. Nor are you likely to suddenly become a master of in character role playing without practice. So view interacting with the rules and with the playing of roles as entertaining learning experiences. In other words: Remember to have fun.
One of the biggest issues with first time gamers is that they don't know what they're "supposed" to do. There generally aren't one or two obvious options with clear consequences, so they tend to get option paralysis. And that's fine. It happens to all of us. The most important thing is that you choose something you think is interesting that you think will be fun for the group; it doesn't matter if you choose the "right" course of action. So jump in and make a splash.
Now, rules. There are a bunch. Let's look at the very most basic bit of rules: a skill roll. You roll four Fudge dice, then add the rating of a single skill. How hard is the roll? Look at the rating ladder, and check out the adjectives. So, Average (+1) is the difficulty for a roll that a person who is average at that skill will succeed on most of the time (average in this case generally being average for someone who has actually received some training in that area). This part is really simple, and you can use common English adjectives to guide yourself.
Now for Aspects. These are things that are true about your character, at least in a narrative sense. "Built like an ape," for example. Okay, so the thing to remember about Aspects is that they don't come into play unless someone is willing to push some fate points around the table; they're not set modifiers. Being built like an ape doesn't help or hurt you unless fate points change hands. If the GM wants to say that your massive size means you can't go out on a fragile walkway, the GM needs to give you a fate point for that. If you want your dude who is built like an ape to be better at intimidation because of it, you need to spend a fate point.
The chapter on Aspects covers exactly how they work pretty well, so I won't go into it.
This stuff is what I consider to be the basic bits of playing a FATE game. There's a bunch more, but this stuff is the entry level. I have run games with very little more than this, and they went fine. If you learn this stuff, you'll have the basic stuff you need to get into the additional rules.
If any of this is unclear, please feel free to ask. Meanwhile, go explore this stuff with your new gaming group. Remember to have fun, even if you're pretty sure you messed up the rules. Fun is the important part.
