To ascend in the Halo 3 ranks one must acquire Experience Points (EXP) as well as a Matchmaking Skill Level (MSL). Note that MSL has no bearing until you make it to the Officer Rankings. One can gain EXP by playing in the Social Playlists which is not ranked and therefore will not increase your MSL. To obtain the Spartan Officer Achievement you will need to play in the Ranked Playlist until you get to MSL 10. EXP is distributed as shown below.
Team or top half of FFA: Win = +1, Loss = 0, Quit a match = -1.