If a tampon causes a clog inside your toilet bowl, plunging the toilet will only push it farther down the drain where it can cause a more serious problem. Attempting to break it apart with a snake not advisable either, because even in pieces a tampon can clog in the waste line. The best way to remove a tampon is to pull it out.
Flush the toilet to clear as much of the water from the bowl as possible. If the toilet drain is stopped completely, put on a pair of rubber gloves, preferably ones that cover your forearms, and use a cup to empty some water from the bowl into a bucket to prevent the bowl from overflowing.
Insert a plumbing snake into the drain opening and push it in until it won't go any farther. Crank the handle once or twice to work the head into the tampon, then pull the snake out. Hopefully, it will bring the tampon with it. If this doesn't work the first time, try again. If the snake doesn't pull out the tampon, it may move it enough to allow water to drain from the bowl.
Reach into the drain and pull the tampon out by hand if you can't do it with the snake. If you can't find it, it may be stuck in the upper part of the P-trap and out of reach.
Turn off the water to the toilet and unscrew the supply connection from the bottom of the tank. If the bowl is still full of water, empty as much as you can into the bucket, then flush the toilet to empty the tank into the bowl. Transfer this water to bucket.
Unbolt the toilet from the floor with a wrench and lift it off the drain. Set it on plastic sheeting in another part of the bathroom or take it outside. Tilt it carefully, sponging up water that spills out as you do. When you can, reach into the bottom and pull the tampon out from the P-trap.
Check the waste line if you can't find the tampon in the toilet. It may be lodged just past the waste opening where the pipes curve into the main stack. Pull it out by hand if you can, or try pulling it out with the snake. You may also be able to reach it with a pair of tongs or a long screwdriver.
Clean off the old wax from around the toilet flange with a putty knife once you have successfully retrieved the tampon and set a new wax ring in place on the flange. Set the toilet back in position, bolt it to the floor and reconnect the water line. Turn on the water and flush a few times to make sure everything is working properly.