Forget the old way of replacing the broken I phone 3 screen without the frame! You can now purchase the glass screen with the frame, much, much easier and a better way to fix the broken screen.
Purchase the screen and frame here: Pre-installed Kit : Apple iPhone 3G Lcd Glass Screen Cover + Touch Screen Digitizer + Frame + Home Flex Button + Ear Speaker + Tool + Cleaning Cloth
1) Remove the bottom two screws
2) Use the suction cup to remove the old glass(carefully!)
3) Disconnect the connectors(Carefully)
4) Remove the side screws from the frame/glass.
5) Carefully remove the old glass and frame from the LCD.
6) Install the new glass and frame around the LCD.
7) Re-connect the connectors to the glass/LCD.
8) Re-install the two screws at the bottom of the I-Phone.
9) Turn On.
10) If I phone does not turn on the connectors may not be connected properly.