The right way to role-play: determining your actions from your imagined character's perspective. Doesn't matter if you're full-immersion LARPing, occasionally speaking in character, or just rolling dice to resolve social interactions and tersely describing everything in the third person. As long as actions are determined by character, not player, perspective, it's role-playing.
The wrong way to role-play: meta-gaming. Playing your character not as your character, but as a gamer out to win the game.
That said, there are plenty of stylistic variations which are indeed legitimate role-playing which still irk me nonetheless. Most of them being one extreme or the other. I want no truck with players who get too much into their characters, that they cannot observe the boundary between the reality and the fantasy; and, likewise, the players who just don't give a crap about their characters, the setting, the labor which has gone into the campaign, the DM, or fellow players. Both extremes in my experience lead to a kind of selfish, childish, and really antisocial sort of role-playing, where the player either hogs the spotlight or actively derails the campaign, and where the character is made to act in ways which are downright psychopathic by normal standards.
In short, "right" role-playing is simply not meta-gaming. "Good" role-playing, the best role-playing, comes from a mature respect for one's fellow players and for the work that the DM has put into the campaign.