EzekielRaiden
Follower of the Way
For me, the core of roleplay revolves around determining a character's values and personality quirks, and then immersing myself in them until they become as natural as my own verbal tics (like saying "basically..." or "essentially..." all the gorram time, ugh I hate that I do that so much but cannot stop myself).
This is one reason why I tend to play one of a stable of "familiar" characters. I've grown used to their personalities--I know them like one knows an old friend. Of course, it can be rewarding to be pushed into something new and unfamiliar as well, even if it means such characters have a tendency to show...indecision unbecoming of their otherwise-established personality traits
After that, it's a matter of putting just enough twists and inflections to make things feel textured without bogging down play. A lot of it can be done purely through word choice. As an example, the character I'm currently playing in a science-fantasy 4e game, Seth. He comes from a race that disappeared--a long, long time ago, but somehow he was spared that disappearance while in a healing stasis, only to be "recovered" by (corrupt) corporate xeno-archaeologists in the present day, and then subjected to experiments to determine how useful he might be (among other things). One such experiment psionically implanted knowledge of the current trade language in his head--and, since the nominal government of this region of space IS a mega-conglomerate (whose subsidiaries constantly compete with one another, sometimes even to the point of open combat!), that basically makes it the Common Tongue of this setting. But because this knowledge was implanted, rather than learned naturally, he has some odd or unusual inflections; he tends to speak in a mildly archaic fashion, and generally avoids using conjunctions. So, for example, if asked a yes/no question, he'll probably respond with "aye" or "nay" instead. It's not enough to make him difficult to understand at all--but it gives a subtle flavor of being old-fashioned, even medieval, which is perfectly in keeping with his backstory.
I've also worked to give his culture a light but consistent sketch. For example, all of the proper names I've used have originated in Hebrew (Biblical or Modern) or Arabic. Mechanically, he's a Dragonborn, but narratively, he is one of the Or'im (literally "Lights" in Hebrew); he considers his companions Epher'im (literally "dust" or "ashes," but the meaning he gives it is more like "my adopted people") and worships Bahamut (from the Biblical Hebrew BHMVT, a great beast shown to Job). And mechanically, his class is Paladin; narratively, precisely how his abilities work is left obscure. This ambiguity is intentional on both my part and the DM's, as he specifically wants to leave questions of gods and the divine open-ended. Magic--rather, "Arcanics"--is considered a branch of science. Whether any given culture's abilities or techniques are "divine," or in truth some application of esoteric and obscure technology is thus a difficult or even impossible question to answer--my character certainly believes that Bahamut is a god (perhaps even the, i.e. monotheistic, god), but whether that is fact or not is open-ended.
Attention to these things, the cultural factors, the personal beliefs, the bearing and demeanor of a character, is the heart of roleplaying in my opinion. It is how a character goes from being simply a collection of data into being a role one plays extemporaneously.
This is one reason why I tend to play one of a stable of "familiar" characters. I've grown used to their personalities--I know them like one knows an old friend. Of course, it can be rewarding to be pushed into something new and unfamiliar as well, even if it means such characters have a tendency to show...indecision unbecoming of their otherwise-established personality traits

After that, it's a matter of putting just enough twists and inflections to make things feel textured without bogging down play. A lot of it can be done purely through word choice. As an example, the character I'm currently playing in a science-fantasy 4e game, Seth. He comes from a race that disappeared--a long, long time ago, but somehow he was spared that disappearance while in a healing stasis, only to be "recovered" by (corrupt) corporate xeno-archaeologists in the present day, and then subjected to experiments to determine how useful he might be (among other things). One such experiment psionically implanted knowledge of the current trade language in his head--and, since the nominal government of this region of space IS a mega-conglomerate (whose subsidiaries constantly compete with one another, sometimes even to the point of open combat!), that basically makes it the Common Tongue of this setting. But because this knowledge was implanted, rather than learned naturally, he has some odd or unusual inflections; he tends to speak in a mildly archaic fashion, and generally avoids using conjunctions. So, for example, if asked a yes/no question, he'll probably respond with "aye" or "nay" instead. It's not enough to make him difficult to understand at all--but it gives a subtle flavor of being old-fashioned, even medieval, which is perfectly in keeping with his backstory.
I've also worked to give his culture a light but consistent sketch. For example, all of the proper names I've used have originated in Hebrew (Biblical or Modern) or Arabic. Mechanically, he's a Dragonborn, but narratively, he is one of the Or'im (literally "Lights" in Hebrew); he considers his companions Epher'im (literally "dust" or "ashes," but the meaning he gives it is more like "my adopted people") and worships Bahamut (from the Biblical Hebrew BHMVT, a great beast shown to Job). And mechanically, his class is Paladin; narratively, precisely how his abilities work is left obscure. This ambiguity is intentional on both my part and the DM's, as he specifically wants to leave questions of gods and the divine open-ended. Magic--rather, "Arcanics"--is considered a branch of science. Whether any given culture's abilities or techniques are "divine," or in truth some application of esoteric and obscure technology is thus a difficult or even impossible question to answer--my character certainly believes that Bahamut is a god (perhaps even the, i.e. monotheistic, god), but whether that is fact or not is open-ended.
Attention to these things, the cultural factors, the personal beliefs, the bearing and demeanor of a character, is the heart of roleplaying in my opinion. It is how a character goes from being simply a collection of data into being a role one plays extemporaneously.