I know most phones do these days, but this one isn't advertised as such. I'm wondering whether or not this is merely an under-sight as far as noting of features.
Yes; the phone is equipped with a WAP browser. To access the browser, from Idle mode, press the Menu softkey; scroll to the T-Zones icon (or other WAP browser icon if your carrier is not T-Mobile); press the Select softkey to enter the menu. The "Home" option connects the phone to the netowrk and loads the T-Zones home page (or whatever page you have set up for your home page).
From the Menu, choose "Go to URL;" from this page you can enter an address and then press the OK key to go there directly.
I highly recommend downloading the manual for your phone; it's much easier to locate things since it's a PDF file, and is searchable. You can get it for free at http://www.phonedog.com/cell-phone-research/samsung-sgh-t429_user-manual.aspx - just click on the link below the pictures of the phone ("Click here to download the manual" in blue lettering).