Answer:
If you aren't getting any internet access whatsoever, then you should make sure the iPhone has been activated with AT&T.
If you are only getting a connection through "Edge" (the letter E will appear in the top bar), then you are either not in an area that has 3G available or it is simply disabled.
To make sure you have 3G enabled, go to Settings > General > Network. If the "enable 3G" button is off, turn it on. If it IS on, but you aren't getting 3G coverage in places you normally do, I would contact AT&T.