When preparing to sharpen your reel mower, you usually need to remove what is called the "C" or "E" clip, shaped to look like either letter. It's usually situation on the wheel assembly. Use a flat-head screwdriver to slip underneath the clip and pop it off. Once it's removed, the wheel and pinion gear slip off so you can access the blades.
Reel mower sharpening kits come with the backlapping tool. This tool is placed over the shaft where the pinion gear sits. This tools turns the blades during the sharpening process. Keep turning the backlapping tool counterclockwise until the blades feel sharp and appear smooth.
A paintbrush is also provided with a reel mower sharpening kit. Along with the paintbrush is a sharpening compound. Apply the compound to the blades, using the paintbrush before you turn the backlapping tool. Use a kit that supplies a compound between 100 and 240 grit. Coat the blades completely to sharpen the blades properly.
After sharpening, test if the reel mower is sufficiently sharpened. Place a piece of paper between the blades and turn the blades to cut the paper; the cut should appear clean with no jagged edges. If these tools do not sharpen the blades effectively, have the blades professionally sharpened by a lawn mower repair service.