Fastest way to level up?

That's pretty much how you get xp.

Occasionally theres missions that give xp (on top of FWOTD which you should also strive to get), but it's basically play games, and potentially have boosts. XP/time is similar between modes, although spamming TT bots for near guaranteed 7 minute wins all day is probably the fastest xp possible. Not by a huge margin though, so it's probably far less mind numbing to just play normally.

Fastest way to level up, without playing the game? Not sure exactly what you mean by that, but its against the ToS.

Eat your Wheaties. [sg-poppy]

Buy a boost and play spam intermediate twisted treeline. Fastest xp per hour that I know of.