You typically have two or more teams playing against each other, each bowling their own 10 frames of games (like pattycakes said, three is a good number). At the end of the night, you average the team member's scores together to determine which team is in the lead. You can also average each individual's scores together to determine each person's individual averages (so the person can see how they've improved, and to determine handicaps, if you want to do that).
For fun, you can have little prizes (in league, you get patches or trophies if it's a special tournament) or special titles for certain achievement markers, like "High Average" or "High Game." When I was in the league, you also got individual awards for beating your own best game -- like playing 160, 200 ... 240, 260, and the like. That gives each person an individual as well as a team motivation.
I like Ahorsesoul's idea to call a local alley for a brief overview. Otherwise, you can browse here:
USBC Official Rulebook.
If there's a night when you tie or want to speed through a game, you could play this way:
"The Baker System is a modified format consisting of teams of two or more bowlers.
a. All team members follow each other in order, each bowling a complete frame, until a complete game is bowled.
b. Ten frames are combined to calculate a team game."
I'd forget about adding handicap to the game because it's complicated. Besides, you can't even calculate the handicap until you've established an average (either from a previous season or after a few games into the season...), so might as well skip that step. I'd just bowl the three games (or depending on how many people you have and how long you want to spend bowling, you could switch that up), average out the team and individual scores (and keep a record near your Wii for people to peek at and watch their own progress), and have fun.