In my first campaign I've tended to approach RP casually. Its fun to imagine what the scenery would like up close and in more detail as you wander endlessly around the map's different climates, picture your army moving as an actual mass of individual soldiers and supplies, that sort of thing. As far as how RP informs my actions, I've gone with "what would I personally do in this situation?" Or at least "what do I THINK I would do?" rather than a pre-created fictional persona, mainly because I didn't want to be too restricted my first time through the game.
For my 3.6 campaign I actually do want to try RPing as a character, which I think will be more fun now that I have a better understanding of (roughly) what to expect at each stage of the game.