Work a razor blade under the silicone at a low angle, as though you are trying to scoop it up. Cutting the silicone at this angle helps you avoid cutting or otherwise damaging the edge of the tub. Work your way around the entire seal, cutting out the silicone from underneath. Focus on separating the silicone from the tub and wall--it doesn't matter if it is still attached to the glass door.
Carefully wiggle the door loose until it pops out of place. Depending on the framework on which your door sits--for example, if it swings out or slides--you may need to unscrew the metal frame that holds it in place. For example, a glass shower wall may be held in place by a metal band that runs across the top of the shower like a curtain rod, connected into either wall. You may need to unscrew that from the wall in order to remove the door. Inspect your own shower wall and door to determine whether or not that is necessary.
Mix 3 quarts of warm water with 1 quart chlorine bleach and 1/3 cup powdered laundry detergent. Use this solution and a clean cloth to wipe down the spots where the silicone was, letting it soak for 10 minutes. Then wipe it down with rubbing alcohol, and wipe it dry to ensure it is thoroughly clean.
Slide the replacement glass into place. Again, depending on the type of enclosure you have, you may need to put the glass in place and then frame it with a metal band. Follow the installation instructions that came with your door to ensure that it is properly installed.
Press the opening of a tube of caulk into the crevice between the glass and the tub and/or the glass and the wall. Squirt caulk into the crevice, sealing the two together. If you want a smooth finish, wipe your finger along the caulked crevice to smooth out the sealant. Remember to caulk the door on both the inside and the outside.