It is very important to remember that Mario Strikers is the first online game for the Wii, and it should really be assessed in that light.
The online aspect has two sides to it a Ranked Match and a Friendly Match, when you choose a Ranked Match you are pitted against another person in your region, you play best of 3 matches and are awarded points based on if you win, how many goals you score and so on. The Stadium that you play in is randomized, but you can still pick your own captain and sidekicks.
The points attained in a Ranked Match go towards a regional leader board, the season lasts a week after which point it is re-set, you can have a look at the leader board to check your ranking, the top ranked players and your friends rankings. There is a striker of the day award for the player with the most points in your region.
A Friendly Match (against people on your friends list) is unranked and no points are awarded, you can play a Friendly Match against anyone anywhere in the world (of course at the moment only Europeans have the game). You can also adjust the parameters of the game (i.e. Classic Mode, with no skill shots) and choose the stadium you want to play in.
There isn't an undue amount of lag when playing Ranked Matches, and you have the option to accept or reject an opponent based on the connection quality (represented by stars). Of course as there are no Servers involved when playing the game (apart from the initial matchmaking), the quality of game you experience is dependant on the quality of you and your opponents Internet connections (just like Xbox live).
The only negative is that there is no voice chat, so you cant taunt an opponent which sort of zaps some of the fun out of the game for me.