I am completely remodeling my bathroom and the old toilet was ugly and wasted a lot of water, so I decided to replace it with a new water efficient model. Water efficient models maybe a little more expensive on up front costs, but the long term saving for the planet and your water bill are worth it.
Step 1: What You Need...
A toilet with any nuts, bolts, etc. that come with it
A wax toilet seal (It's round, made of wax, and is usually easy to find in the plumbing section of any store that also sells toilets)
A crescent wrench
A toilet seat/lid (if your toilet doesn't come with one. Toilets usually have very standard sizes, just remember to check what type of bowl your new toilet has)
Step 2: Setting in the Bowl
Carefully turn the toilet upside down. Squish the wax ring around the hole, being careful to make sure it seals all the way around. This is important if you don't want the contents of the toilet flowing over the floor.
Around the drain hole there will be a metal ring attached directly to the floor with two bolt sticking up. If you are replacing the toilet, it is usually fine to reuse those bolts.
Being careful not to drop the toilet, turn it back over setting on the bolts (there will be holes in the base of the toilet for them)
Now, put the nut and washer on the bolt. Do not over tighten or the toilet will break. Tighten nuts until snug. Repeat on the other side.
Step 3: The Tank
On many modern toilets the inner workings of the tanks are pre-installed, so all you have to do is set the tank on the bowl and attach the hose for water. The water hose is attached to a a valve that will be off. It should be fairly obvious where to attach the hose on the back of the toilet (it will just screw on). Turn the valve on.
Congratulations, your toilet should work now.
Step 4: The Lid
Installing a toilet lid is quite simple. Set the lid on the bowl of the toilet. The holes in the hing of the seat/lid should line up with the holes in the toilet. With the lid should be to bolts that fit in the holes previously mentioned. Screw on the nuts snugly but not too tight. Snap the miniature lid over the head of the bolt.
If you've done everything right now your toilet is fully functional!