Replacing an existing toilet is easier than one might think. First, measure the distance from the wall to the rear floor bolts on the foot of the toilet. If you measure 12 inches (1 ft.), you are in luck and have a standard toilet size. Sometimes, in older houses there are not standard distances, so make sure you measure before you head to the store.
Once you have your new toilet, it is time for removal of the existing one. Turn the water off at the supply valve, and flush the toilet to empty the tank. Remove any remaining water with towels and sponges, and use gloves. Remove the tank bolts and disconnect the water supply line. Straddling the bowl, lift the tank off of the toilet, making sure to bend at the knees. Remove the nuts from the floor bolts by removing the protective cap and using a crescent wrench to back off the nuts.
Carefully rock the bowl back and forth to unseat it from the wax seal, and lift up to clear it from the studs. Using a putty knife scrape the old wax seal off of the floor mounted flange (you may want to replace the flange at this time, if your old one was damaged).
Seat a new wax ring onto the floor flange. Place the toilet bowl over the flange, align the holes in the toilet foot with the studs, and set the toilet into place. Rock the toilet back and forth to seat the wax ring, and then tighten down the bolts on each side (alternate back and forth between bolts, to keep the toilet level).
Reattach the tank by placing it back into position with the tank bolts dropped through the holes in the bowl. Tighten down the bolts and reattach the supply valve. Install the toilet valve assembly, and caulk around the foot of the toilet to seal the base.