Turn off the water to the toilet. Flush the toilet and hold the handle down to empty the tank. Disconnect the water supply hose from the valve, using adjustable pliers if necessary.
Unscrew the bolts holding the toilet to the floor with a wrench and lift off the toilet. Take it outside and turn it on its side to dump out the water, then scrape the wax from the bottom with a putty knife.
Scrape all the wax off the flange ring using the putty knife, then unscrew the bolts holding it to the floor with a screwdriver.
Make a cut through the ring with a hacksaw. Pry a stainless steel ring away from the rest of the flange with a flat-head screwdriver, working from the cut toward the other side of the flange. If the flange is cast iron or plastic, make several cuts with the hacksaw and pry it off in pieces.
Set a stainless steel replacement ring over the flange and set its lip into the groove of the flange body. Rotate it until the tracks for the bolts are in the same orientation as the those on the ring you removed.
Bend the claws on the ring into the groove on the flange, using a flat-head screwdriver. After clamping the ring to the flange in this way, screw the ring to the floor using the screws you removed from the old flange.
Slide a new pair of toilet bolts into the tracks and position them opposite each other. Place a new wax ring on the flange with its tapered side facing up so that it will fit snugly in the toilet outlet.
Set the toilet back on the flange, guiding the bolts through the holes in the bottom of the toilet. Sit on the toilet to compress the wax ring, then replace the nuts and tighten them with the wrench.
Hook up the water, turn on the valve and let the tank fill. Flush the toilet once or twice and check for leaks around the base.