I'm not a plumber but I have done this many times and it can be pretty easy. Turn off your toilet's supply water, flush the toilet, put on your heavy rubber gloves, then get as much of the water out of it as you can by bailing/sponge etc.. This will minimize the amount that will pour out when you pull it up. Disconnect the supply from the toilet (If you can get away with not having to disconnect the metal compression fitting near the supply handle then don't do it because then it is best to get new parts etc. - compression fittings can be tricky to install leak free for non-plumbers. Take care to not bang into the supply during construction or you may get a leak. If you need to re-do the compression fitting then maybe do another post asking only about this.), pop off the plastic nut covers at the base of the toilet, remove the nuts and washers and SAVE THEM. Wiggle the toilet from side to side to try to loosen the wax seal (after taking off the tank lid so it doesn't fall off and break in half) then lift the toilet straight off and put it down on its side on top of some plastic sheeting (This involves giving your toilet a big hug which is not for the squeemish and can easily throw out your back), mop up the mess from the water that glugged out, clean all the old wax off the bottom of the toilet and the flange on the floor. You should probably remove the bolts from the flange before you lose them. These just slide in their "keyhole" slot and come straight out. Stuff a rag into the hole in the floor to prevent sewer gasses from entering your house. Now throw away your rubber gloves and wash your hands with anti-bacteria soap twice.
The flange on your floor is the end of the drain plumbing. It is screwed into your floor. If the finished level of your floor is raised very much with your new floor then you should probably raise the flange too, shim it, and screw it back to the floor. If you are only raising it a little (1/4") then you probably don't need to mess with it. After you install your new floor, then get a new wax ring and put it on the toilet. Some people also use plumbers putty. If you have raised your floor then you may need an extension flange insert and longer flange bolts. If not, then your old bolts will work fine. Slip the bolts back in the keyholes on the flange and slide them around to 9 and 3 O'clock, you might want to slip in some plumbers putty to stop them from sliding around too easy while you are trying to put your toilet back on. Now you have to lift up the toilet (big hug) and place it precisely on the flange, using the bolts for guidance. Take care to get the bolts smoothly through the holes in the toilet base without letting them slip out of their keyhole etc. Unless you are big and strong, you might want to try this with two people. You don't want the wax ring to mush unless it is right on the flange or you won't get a good seal. Sit on the toilet to compress the wax. This may take a little while, resist trying to rock it. When the toilet finally reaches the finished floor then it is time to put the washers and nuts back on the bolts. Resist trying to tighten these too much because it is very easy to crack your toilet. Re-connect the supply and you are done.
Good schematic drawing at: http://www.popularmechanics.com/popmech/homei/9602HIHOM.html
Some decent how to: http://www.popularmechanics.com/popmech/homei/9704HIHIBP.html