You can find and invite people on Zynga. We are in the era of social gaming. You invite friends to Zynga Poker by entering their individual friend codes. If you’re playing the Facebook edition of the game, you can just invite them via their profiles.
To make random people buddies, then simply click on their avatar, go to “Add Buddy”. You should see an animation of a mail flying from you to your request. If they accept, then you two should be buddies.