The trickiest part of tiling a bathroom floor is dealing with the toilet. There is almost never an instance in which you'd want to tile around the toilet, so you have to remove it, tile the space under it, and then reset the toilet. Removing, or "pulling," a toilet is a messy, unpleasant job, but trying to tile around it would cause far more trouble in the long run. How you make those curved tile cuts around the toilet drain will be determined by what kind of tile you're laying.
Turn off the water supply to the toilet by closing the valve at the wall behind it. Flush the toilet several times to empty it. Use pliers to disconnect the water supply line at the bottom of the toilet tank.
Remove the mounting nuts that are holding the toilet base to the floor. Lift the toilet straight up and move it out of the room. Remove the old wax sealing ring from the bottom opening of the toilet. You will be left with just the toilet drain in the floor, and a flange around it.
Lay out and install the rest of the tiles in the room, leaving the area immediately around the toilet flange untiled.
Lay loose tiles over the flange in the position they will go in relation to the rest of the tiles. Use your wax pencil to mark curved lines on the tiles to show where they will sit around the flange. (You'll be able to see the position of the flange through the spaces between the tiles.) Make your curved marks about 1/4 inch out from the edge of the flange.
Cut around the curves with a wet saw if the tile is stone. If the tile is ceramic, use tile nippers to chip and break off pieces of the tiles until you get to the curved lines. (Note: The tile cuts don't have to be perfect, since the whole area is going to be covered up by the toilet.)
Spread tile adhesive around the toilet flange. Set the cut tiles in place. Let them set overnight.
Grout the floor, spreading the grout with a grout float, pressing it into the lines between the tiles and then wiping off the excess with a damp sponge. Don't grout the space between the curved cuts of the tiles and the toilet flange. Let the grout set for a day.
Run a smooth bead of caulk in the space between the cut tiles and the toilet flange, pressing the caulk against the cutaway base of the tiles to prevent moisture from getting under them.
Reset the toilet in place, setting your new wax sealing ring around the opening on the bottom of the fixture to seal the toilet drain. Reinstall the mounting bolts and water line.
Run a thin bead of caulk around the toilet base, where it meets the tile.
If the toilet flange is the only curved cut you have to make in the room, and you're using any tile other than ceramic, it isn't worth buying or renting a wet saw. Just mark the cuts and take them to your local home improvement store, where they can make the cuts for you.
Wear eye protection when cutting tiles.