iPod touch Play games without wifi?

Hey everyone! I just got an iPod touch tonight. I'm wondering if it's possible to play games without wifi access. When I click on the game center, it asks for my apple ID and pw, which I enter, then nothing happens.

Is there an initial internet requirement, then I can play without internet, or? Kind of bummed if I need a constant wifi connection to play games... so any help would be great. I tried searching but must not be putting in the correct search terms. Thanks a lot. I've got old iPods that are sooo basic compared to the touch, so I'm a little overwhelmed.

If it helps - I only downloaded three apps so far, words with friends, angry birds, and the talking tom. One more question, I don't know where to find the talking tom app, or is it in the game center?

Oh! Thank god for that. Well, I did download them and have them auto synced, so I'm wondering why I don't see them... or if they're hidden somewhere :/.

Ah, I didn't realize I had to drag and drop games onto my iPod in iTunes, odd, I think I got em working now . Thanks for your help!