A lot of the online casinos are set up so you can play using "play money". I play at a site called www.pacificpoker.com using play money. I don't think I even had to give them a name to register, much less any personal information. You play in real time against other real players, and I think they offer Texas Hold'em and Omaha Hi and Omaha Hi/Lo. (I don't know anything about the differences, cause I'm a novice at this--I just play Texas Hold'em)

Here's a link to an online poker glossary:

http://www.pokerpages.com/pokerinfo/glossary/glossary-a.htm