I think I won 2 or 3 other NeoGAF races a dozen minutes ago. That adds to the one this morning (PAL land)
It's pretty much like true racing (with warmups etc) when you go online, you have to stay for several races to hope to win (with good players at least I mean).
First you have to race your way to the 3-4 first places on the start line when you begin a race. Then the first half a lap is very important to position yourself out of the pack, and collect enough coins.
If you manage that, you're probably 1st or 2nd and then without driving errors you have a chance to win.
It's not a general rule but that's the way I feel the game online so far.
It's not broken like Mario Kart Wii or DS, where you had to be 1st and all the others players were pounding themselves in the pack, allowing the driver in 1st to quietly win his race far ahead.