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Shut off the water supply at the toilet valve. Drain the tank by flushing it. You may need to operate the flapper valve manually to prevent an overflow. Then use a plunger to remove as much water as possible from the bowl. Place a towel behind the toilet to absorb spills.
Remove the water supply from the threaded inlet on the bottom of the tank. Take off the bolts from the inside of the tank, and lift the tank off of the bowl. Remove the bolts holding the toilet to the floor, and lift the bowl straight up. The wax seal underneath may hold the toilet in place to some extent. Remove the clog from the bottom of the toilet, or clean out the drain underneath.
Place a new wax ring around the drain flange (Pictured). It will help level and seal the toilet. Don't try to reuse the old ring. Replace the toilet by reversing the process you used to remove it.
Broken seat bolts are a common problem with toilets. Replacement bolts are available at most hardware stores.
If your toilet runs nonstop, you probably have a leaking flapper valve. Chlorine in the water causes rubber valves to deteriorate and curl upward over time. To test your flapper valve, pour some food dye into the tank. Check the bowl a few hours later. If you see dye in the bowl, you need a new flapper valve.
If the handle breaks, simply remove and replace it. Make sure the chain on the handle is tight enough to pull up the flapper valve but not so tight that it prevents the valve from closing properly.
If your ball-style float valve is damaged, replace it with a new one (Pictured). New valves are more efficient and tend to last longer.