Watch this video from This Old House to learn how to fix a wobbly toilet.
1 Turn off water to toilet by closing shut-off valve.
2 Flush toilet and hold down the lever to empty tank.
3 Sop up remaining water from tank and bowl with sponge or turkey baster.
4 Use adjustable wrench to disconnect the water-supply line from toilet tank.
5 Remove the caps from the closet bolts on each side of the toilet to expose hex nuts; use an open-end wrench to remove the nuts.
6 Lift up the toilet and set it on newspaper or cardboard.
7 Scrape away the old wax ring with a putty knife.
8 Stuff a rag in drainpipe to block sewer gases.
9 If necessary, use hammer and cold chisel to chip away tile to expose the closet flange.
10 Slip a repair plate under damage section of closet flange.
11 Install new closet bolts into slots in closet flange.
12 Press new wax gasket onto closet flange.
13 Set toilet back into place; press down to compress gasket.
14 Tighten nuts on closet bolts.
15 Trim bolts with hacksaw.
16 Install bolt caps over the closet bolts.
17 Check to make sure toilet is tight to floor and doesn't rock.