Just like the one ring to rule them all, there is one act to rule them all in improving your "role play" (and yet, just as there were many rings beholden to the one ring, there are many pieces to this act):
Dive into, and play according to, your character's persona.
More important than anything else in role-playing is to build a character persona. Who are they and how do they see the world around them? Figuring that out will help you to understand how they will act or react in given situations and how much the results of those situations will affect them going forward.
People always start with backgrounds ... and that's good, but the point of a background isn't just to give people something cool to think about. It's to build a reason for why your character's persona is what it is. It helps you flesh out how they think, what they do, who they trust, and what is important to them. THAT is the important part.
Think of a very basic character goal before you do ANYTHING else in your character creation. It should be really simple, giving a pretty straight forward sort of 'mission statement' of your character:
* Protect the downtrodden
* Discover of hidden knowledge
* Seek redemption for a prior heinous act
* Quest for glory
* etc
A primary motivating factor is very important. It helps color all of your decisions.
Next, come up with a very basic description of the character:
* sheltered academic
* barbaric shaman
* religiously-devout noble
* selfless street rat
* etc
Now you've got what you need to build a backstory. You have a motivation and a 'who you are'. Start thinking of what made you who you are, and especially what might bring your character to the starting point of the campaign.
With both of these things figured, and at least a basic background thought up, you can start building your statistical character. Use this opportunity to further flesh your persona. Did you roll poorly for one stat? Which should it be? Why? If point buying ... why are you putting more points into one stat than another? Are you using one or two stats as 'dump' stats? Why? ANSWER EVERYTHING IN STATISTICAL CHARACTER CREATION THROUGH YOUR CHARACTERS PERSONA. Give them a REASON for having skills and feats ... and, in fact, if a skill or feat does not make sense for what you've built persona-wise, do not take it. If you've built a real persona, you're not going to "gimp" yourself ... you're just going to build a character that makes sense.
With your statistical character fleshed out, you should have enough of an idea of who you're about to play. At that point, it's all about "getting into character". Challenge yourself to think in the mind of your character ... "dive in" to your persona.
* Are 20 ft. rock golems something you see every day? Or are they something you may be cautious of charging into melee with?
* Do you like or trust the mayor who wants to send you on a quest?
* You've just spent a whole day slogging through the rain ... is your character REALLY doing just fine even though no hit points have been lost? ( I'd argue they're probably in a pretty rotten mood )
* You just found a huge pile of treasure ... what are you going to do with it? Build a castle? Take care of mom and dad? Give it to the poor? Donate to your church? Spend it on beer and women (or men)?
Think of every situation as your character would think of the situation, not as you ... the player of many games who knows what his/her DM tends to do ... would think of the situation.
Ok ... my second tl;dr post of the day ... I'm stopping here ... I've got more to say but I think the basic premise is there.
Last note ... one of my least favorite things in gaming is when the battle mat comes out and people start talking to each other "If you move 3 squares that way and circle around here we can flank goblin 23". Why not "Kelthor! Get around and flank this bugger!"? Seriously. Same thing ... one is ridiculously "game-y" and the other is role-playing.