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There are a variety of tools you can use to remove the caulk, but it's most effective to slice it off with a razor scraper, utility knife, or five-in-one painter's tool. Using quick, sharp strokes, slice under the length of all old caulk beads. Go along each edge of the caulk with your blade to get it removed.  If you are caulking a new shower, there won't be any caulk for you to remove. Note that metal blades and chemical caulk removers can damage plastic tubs. Use a plastic blade if your tub or shower is made of plastic. Once you have loosened the caulk with a knife, pull it off using your fingers. In most cases, if you sliced along both edges of the caulk thoroughly, you will be able to grab one end and pull a long strip out all in one piece. If you can't get a section out easily, cut along the edges again and try to pry it out with the knife. After you slice off the majority of the caulk, there will likely be some small pieces left on the walls. Scrub the sides of the shower with a dry, nonabrasive pad or sponge to remove as much of the old caulk as you can. Follow that by wiping down the surface with rubbing alcohol or scrubbing it with a multi-surface cleanser to remove any remaining caulk, shower scum, or grease.  If your old caulk was made of silicone, use a pad or rag soaked in mineral spirits to break down any remaining bits of caulk. Use a soft rag and not an abrasive one, so that the shower surface is not scarred. Use a damp, clean rag to wipe all seams. This will remove any cleaner, caulk dust, and other dirt from the area. Then dry down the area thoroughly with a dry rag, hair dryer, or paper towels. You can also simply let the area sit until you are sure the seams are all completely dry. If you leave debris or dirt on the surface, the new caulk will not stick as well and not last as long. Place a strip of tape on either side of each joint being caulked. The lines of tape should run parallel to each other and be spaced roughly 3/8 inch (9.5 mm) apart from each other. The tape is being used to help keep the bead of caulk straight and uniform.

Summary:
Slice away any old caulk. Pull out loosened pieces old caulk. Clean out any debris and residue in the seams. Wipe the area down and then let it dry. Line the joints with painter's tape.