Games like Tetris, StarFox, Mario Kart, Metroid Hunters they all do random match ups for you no sweat. And for the most part only sticks you with people of your skill level. One on One matches, or matches between select friends only happens through Friend Codes.
Other games like Contact, Castelvania, Tenchu, Mario Vs. DK, Animal Crossing, only let you trade levels, items, or visit each other, but do NOT have a competitive online portion.
Assuming there are users out there and waiting, you're not likely have any problem and a match (or matches) will be found in roughly 30 seconds or less. But if noone plays the game, like with Contact, Tenchu, Lost Magic, Open Season, or anything in Clubhouse Games that's not BlackJack or Texas Hold'em, then you'll be waiting a long long time for someone to trade/play with.