I didn't know you could do this!
Just go to https://messages.att.net.
It's a little bit clunky and AT&T seems to be deprecating some of it.
For example, you can click on the phone number in a message and a dialog box pops up offering to "Create New Contact" but that doesn't work.
And messages sent from this application don't get pushed back to the phone.
Still, pretty nice.