well on almost all nintendo online com patible games,
on the top left of the games case there is a little blue circle containing Wi-Fi in it
this indicats online functionality (not necisarily online play)
the game should say on the back whether or not it has online play, or just connection,
big brain academy wii, has onlince connection but no online play,
mario strikers charged has online play.
depending on the game the method of getting people to play you is different,
First party games will generally have a friend codes system where you and the person you want to play with add each others codes to play one another,
but some games will let you play a random without the code,
later games will let you play people and then let you add them to your list.
medal of honour heroes 2 will
worms a space oddity will also.
but online play will not be truly good or up and running well untill end of year so thats when online will be better on wii
hope i helped
if i helped you know what to do (rep me please (only if i helped))