Occasionally, objects that shouldn't be there find their way into a toilet, and if they're just the right size, they may get stuck in the P-trap. Children's toys -- especially the squishy or cuddly kind -- are prime candidates for blockage material, because they swell when they get wet. Even small cylindrical objects can be troublesome, because they collect other material, forming a blockage that may develop gradually. Forget about chemicals or plungers -- it takes drastic measures to get something like this out of the toilet plumbing.
It's not fun, and you may not want to be the one to have to do it, but sometimes reaching into the trap and grabbing the obstacle is the easiest way to remove it. No one has to tell you that you'll want to wear rubber gloves that cover your forearms, and you may also want to put on goggles and a mask. If the bowl is full, scoop some of the water into a bucket to prevent overflowing. Reach into the opening, and work your fingers as far into the trap as possible; even if you can't grab the object, you might be able to feel it -- and that's a victory of sorts, because you'll know where it is.
Break Up the Obstruction with an Auger
A -- known to plumbers as a snake -- may be able to break up the object or push it through the trap to the waste opening. Insert the auger into the toilet and push until it won't go any farther. Crank the handle, and then pull the auger back; if the object is soft, the auger head may have worked its way into it, and you can pull part or all of it out. Failing that, push on the cable to force the object the other way. You'll know you're successful if the auger suddenly springs forward and water begins to drain.
Pull the Toilet
An auger can't remove all obstructions, especially those made of wood or hard plastic. The last resort is to lift the toilet off the flange and either pull the object out, push it back through the toilet opening or retrieve it from the waste opening in the floor, where it may have lodged. It's more difficult to pull a toilet when you can't empty it, so you'll probably need a helper:
Turn off the water valve and disconnect the water supply hose from the toilet.
Unscrew the toilet bolts, using a wrench, and lift the toilet carefully. Keep it upright as you walk it out of the bathroom to a place -- preferably outdoors -- where you can safely turn it over and dump the water. Some water will spill, so cover the floor along your path with plastic before you move the toilet.
Pull the object out of the toilet or push it through, using the auger.
Scrape off the old wax ring and fit a new one around the toilet flange before resetting the toilet. Never reuse an old wax ring. Set the toilet back on the flange while guiding the bolts through the holes in the base.
Tighten the screws, and reconnect the water. Fill the tank and flush the toilet to make sure it operates properly.