The most important decisions you have to make about your character are the “here and now” details. You need to know who you are and what you do. I'll go through some of the things that can make a character unique and memorable.
Looks: I want to start with this one, because I think it is something that often gets glossed over in roleplaying. Our first impression of people is based on how they look, so a unique appearance can create good roleplaying opportunities. Is your character well-groomed? Well-dressed? Color coordinated? Do they dress mainly for comfort, function, or style? If you make sure to communicate these things, it will also give your GM something to build NPC's reactions to you on.
Attitude: How does your character treat people? Are they friendly? Suspicious? The difference between brutal honesty and nervous politeness is massive. This is a decision that has to be carefully considered, because it will greatly affect any social event the character is in. There will be times when you as the player knows that insulting the King's adviser would be foolish, but it would be consistent with your character decisions. And that's when good roleplaying means spending the night in the dungeon...
Beliefs: Every person has certain basic beliefs and values. What are your character's? In certain game systems allegiance to a deity is important, but beliefs go much further than that. If you follow a deity, are you a fervent or nominal believer? Conservative or liberal? Monarchist, republican, or anarchist? There are many aspects to a person's belief system, and each one can give you more depth.
Voice: Another under-utilized tool for character building is the character's voice. I'm not just talking about tone or accent (
side note: only do an accent if you can keep it up consistently without it drawing too much attention to itself. Basically, if the other players pay more attention to your accent than to your words, it's not worth it, even if you really want your dwarf to sound Scottish.) but your choice of words. Do you prefer long or short sentences? Do you speak quickly or slowly? Do you have a large vocabulary? Are there certain slang expressions or idioms you like using? What do you say (or shout) when things go wrong? Or when they go right?
Relationships: In order to have depth to your roleplaying, you need to know what you think and feel about the other characters. You should also have some other contacts, friends, and family, because let's face it: everyone has people in their lives. I will talk more about this in part three, but the one thing that's good to keep in mind is to use your decisions about your attitude and beliefs into account when deciding how you feel about other people, both in the party and outside of it.
Personality quirks: Finally, once you have a clear picture of who you are, you can add little details to make your character more rounded out. We all have our little quirks which make us who we are, and they can be both a lot of fun, and useful from a roleplaying perspective. Having your character do odd or stupid things occasionally helps create great memories. Anything could make for an interesting quirk. I used to play with a very laid-back, fun-loving group, and there it was completely appropriate for my character to ask if he could try on people's hats. If you play a more serious game, you can add a more dramatic quirk, like constantly rubbing the scar of your old war injury, or refusing to sleep in the same place more than a single night because you don't feel safe. If you have trouble coming up with something, we have a
thread with ideas you can use. I hope you'll find this useful, and keep an eye on this thread for part three: Knowing Where You Came From.