Turn off water at the supply line and flush toilet to drain water. Put on rubber gloves and remove remaining water using a sponge and bucket. Disconnect water supply line from bottom of tank. Loosen bolts on base of toilet using an adjustable wrench.
Cut the caulk seal around the base of the bowl using a pocketknife. Rock the toilet back and forth to make sure it is loose. Have a friend help you carry it away. Remove wax seal using a putty knife. Stuff an old towel into the opening to block sewer gasses.
Clean the floor around the opening with rubbing alcohol. Apply a bead of caulk around the base of the new bowl. The caulk is primarily to eliminate gaps and make for a neater installation. If there is a significant leak around the wax ring it makes its way through the caulk.
Before putting the tank in place, apply a coat of plumber's grease to the spud washer at the base of the tank. You can substitute petroleum jelly if you don't have plumber's grease. Lift the tank into place and carefully line up the mounting bolts.