All you need is a piece of thin rope and wrench. I wouldn't use an adjustable wrench or vise grips on this.

The goal of almost all clutch removal tools is to block the piston from moving so that the torque you apply to the nut does not go to turning the crank/piston.

1. Remove the spark plug
2. Move the clutch until the piston is approaching the top of stroke, don't go beyond the top of stroke and don't get too close to top of stroke
3. Stuff your rope into the cylinder through the spark plug hole. Put in as much as you can but don't damage your cylinder/piston with any tool you might use to stuff the rope in (i.e. screwdriver).
4. Place your wrench/socket on the nut and turn clockwise. The clutch is always reverse threaded AFAIK. If you look at the clutch it will spin clockwise when in operation. This in turn moves the chain on the top of the bar going away from you and back toward you on the bottom (clockwise). By putting the clutch on with reverse threads, it self tightens as the spindle turns.
5. Hold the saw as best you can. The clutch can be on there pretty good.

Tips: You want the piston beyond the ports when you put the rope in so that you don't end up cutting rope inside the ports when you crank on the nut which will move the piston up it's stroke.

You don't want the piston too close to the top when you put in your rope because you may not get enough rope in the cylinder to prevent the cylinder from reaching TDC and starting it's down stroke. You'll have to start over if you do that. No biggie though.

Put the flywheel/clutch back on in the same manner. Get a decent torque putting it on.

Some people actually do this with only an airgun. I have heard of potential damage doing this but I forget what it was.

The special tools (piston block) they sell for this can cause problems also. The blocks often are small so they can fit through the spark plug hole. The small block can exert enough force on a small area to damage either the piston or cylinder.