Cutting flooring to fit around a toilet flange is not particularly challenging, because any inaccurate cuts will be hidden by the toilet. The most important consideration is to have the surface of the flange come as close to the level of the floor surface as possible, without being at the same level or higher. This method ensures that the wax ring that seals the toilet doesn't leak. If the flange has already been installed, you can use a flange extender to raise it. Extenders come in various thicknesses.
Draw perpendicular lines from two walls to the centre of the flange, using a carpenter's square and a pencil. Measure the length of each line, and the distance from the point of intersection on each wall to the corner, using a tape measure.
Transcribe the measurements onto a sheet of plywood flooring, then make a mark denoting the centre of the flange. Measure the flange's diameter, and draw a circle on the plywood that's 1/2 to 3/4 inch larger in diameter, and centred on the mark.
Drill a hole in the outline of the circle with a 3/8-inch drill bit, then insert the blade of a jigsaw through the hole and cut around the outline. Remove the cut-out circle, then set the plywood into place around the flange. The entire outline of the flange should be visible.
Attach the plywood to the floor in the same way you're attaching the rest of the flooring--with nails, screws or glue.
Measure the distance from the top of the flange to the top of the flooring. If the flange is more than 1/4 inch lower than the flooring, install a flange extender to bring the flange to just below floor level.
Remove the screws holding the old flange to the floor, then place the extender on top of the flange. Rotate the extender until the slots for the closet bolts and the screw holes are exactly aligned. Drive the flange screws back into the subfloor.
The flange should be set just below the level of the floor. Plumbing codes prohibit it being at the same level or higher because it can cause the toilet to rock.