If you find water on the floor, it might be the place where the water connects to the toilet tank. If that's the case, turn off the water, disconnect the leaky connection, wrap it in Teflon tape and retighten the connection. Turn on the water to check if it still leaks. If the water supply feed, a plastic tube, leaks, get a new one.
Hunt for the leak from under the toilet. First, check the bolts that hold the toilet down. If the toilet rocks and won't tighten, you probably need a new flange. If it just leaks, check the wax ring. Turn off the water, flush and bail the rest of the water out. Pull the toilet. Clean the old wax ring off the bottom and off the flange. If the flange is broken, repair or replace it. If everything else looks okay, put a new wax ring under the toilet and set it down on the flange. Tighten it down.
See if the water comes from the place where the tank connects to the bowl. Tighten down the tank bolts that hold the tank to the toilet. If that doesn't work, take it apart and put a new rubber spud washer over the spud boot or a new flush valve. Turn off the water, flush, bail out any left in the tank. Remove the tank bolts and remove the tank. See if you need a new rubber spud washer or spud boot. At this point, it's just as easy to replace the entire mechanism.
If you flush it and water fills the bowl but fails to fill the tank, you have no water source. Check the sink faucet to see if all the water in the house is off or just the toilet. If the sink water works, see if the water shut-off on the toilet is in the on position.
Take off the top of the tank if you press the handle and it doesn't flush. Check the connection between the metal piece and the handle. If it operates with a chain to lift a flapper, make sure the chain isn't tangled or disconnected. You may need to replace the entire mechanism. Turn off the water, flush and bail the rest of the water out of the tank. Remove the tank bolts that connect it to the toilet. Turn it over and use a groove joint pliers loosen the spud nut underneath the tank. Put on the new valve and reassemble.
If the toilet keeps running and has a flapper and chain, it's most likely a tangled chain. Sometimes the flapper that covers the hole where the water runs out of the tank needs replacing. Just clean the seat from all residue. Use vinegar to do this. Then attach the replacement flap valve. Few toilets still have the old ball that raises as the water level raises and shuts off the water at a certain point. If you have one of these and the toilet continuously runs, you may just need to adjust the metal rod that holds the float.
If the seat on an American Standard toilet wiggles and slides to the side, tighten the plastic screws that hold it onto the toilet. If the seat is bad, buy a new one and screw it down with the white plastic screws at the back.