N-Zone magazine has some more specifics on the online modes in Mario Strikers Charged Football.  They also detail how to ‘invite a friend’ in the game:

1. In the online main menu, select the function “Invite a friend”.
2. Now you get a list of all your registered friends. Select the person you want to play against.
3. Your friend’s Wii now displays the following info box: “(Somebody) wants to play with you. Do you want to ..?”
   1. Accept the match
   2. Cancel the match
   3. Accept the match with a friend (= A second player can play at your friend’s console in his team)
   4. Show the match settings (play length, game mode, stadium, cheats on/off)
4. Wait until your friend has accepted the match.
5. The connection quality is displayed and the match starts.

Link