Most DIYers will never have to install a new toilet. However, it is possible that they will have to remove one and then reinstall it at a later date. For instance, when replacing a floor. It is simple to reinstall a toilet, as long as you follow some rules. See the photos below for step by step instructions.

Here you see the closet flange in the floor. The toilet was removed to refinish the wood.
This is the wax ring that will seal the toilet to the flange. Never reuse this ring, always buy a new one. Remove the protective plastic before installing.
Here you can see the wax ring with the protective plastic removed. The black plastic in the middle points down into the flange.
Press the wax ring firmly in the center of the hole.
Here the ring is properly seated. Note the two bolts and washers. They will hold the toilet and prevent it from rocking.
These plastic caps may need to be purchased separately. The nuts and washers are supplied with the wax seal.
Snugly tighten (don’t over-tighten) the nuts so that the toilet doesn’t rock.
Attach your water supply.
Add the plastic caps to give the install a finished look. You have just installed a toilet!