While pulling a toilet up is probably not the most enjoyable way to spend an afternoon, it really isn't overly difficult. First thing to do is shut off the incoming water supply and remove the caulking around the base of the toilet. Then flush or dip out as much water in the tank and bowl as possible, then sponge or vacuum out the rest (using a wet/dry vac) Now disconnect the supply hose from either the tank or the cut off valve. Remove the decorative caps on each side of the base of the toilet to expose the nuts and washers on the flange bolts and remove these nuts. If the nuts and bolts were not brass or stainless steel, they may be difficult to remove and even break when twisted, but they are easy to replace. Once these nuts are removed, the toilet is being held by just the wax ring. Rock the toilet to break this seal and the toilet can be lifted up until it is clear of the flange bolts. You should have several old towels on the floor as there is usually some water left that will run out when the toilet is put on its side as well as gooey remains of the wax ring. With the toilet on its side, you can work from the bottom. I'd clean off the old wax before starting. Clean the flange too. Paint thinner and paper towels will be helpful in the final clean up. After clearing the clog, reset the toilet pretty much in reverse of removal. If those flange bolts need replacing, and the likely will, pay a little extra and get stainless steel. At least don't get coated "rust resistant" bolts. These will corrode eventually. You will need a new wax ring. Avoid the ones with the plastic horn, and use a plain Jane ring. Now the most critical step is the actual placement of the toilet on to the flange. It really requires at least two people because it musts be set straight down, first over the flange bolts and then with the horn on the base of the toilet entering the wax ring square. It sometimes helps to put an extra nut on the flange bolts first to hold the bolts vertical and prevent them from moving. There is plenty of room between the flange and the toilet to do this, but again use stainless steel nuts. Once the toilet is in contact with the ring, use body weight to press the toilet into the ring. A slight twisting will help. You need to make sure the base of the toilet is in complete contact with the floor. Install the washers and nuts on the flange bolts. These should be tightened just to the point of being snug. There purpose is to hold the toilet down, not to pull the toilet down into the ring. Overtightening can break the toilet. Finally, reconnect the supply line and turn the water on. A little floor clean up and caulking around the base of the toilet will complete the job.
