Sequence showing the removal and cleaning of the primary mirror from a Celestron 8 inch Schmidt-Cassegrain telescope.
This starts with the corrector and secondary having already been removed. Next time I clean my corrector I'll take photos and make a gallery for that procedure.
This is one of the older orange tube scopes, the primary had heavy fungus and there was a very dead spider and web in the telescope tube.
If you're reading this, you're either just curious; someone is doing this for you and you want to know just what it entails, or you've decided to give it a try.

If your mirror is merely dusty.....once it is removed try to blow off the dust with a squeeze bulb
or some such, even a hair dryer on NO HEAT. Stand back a few feet and blast it with a CO2 fire extinguisher (no, I'm not kidding).
My point is if it's just dust, blow off what you can and just live with it, a little dust is doing no harm. The cleaning shown here is for serious crud - mainly fungus.

Tools and equipment for disassembly, cleaning, reassembly

::::::for the corrector::::::
Small Phillips screwdriver (not jewellers size, though) for removing the corrector
Fine point tweezers (for grabbing the corrector retainer screws and spacers)
Lint free wipes (plain, unscented bathroom tissue works in a pinch)
ROR and acetone
ROR (Residual Oil Remover) ( http://www.ror.net) Wonderful stuff, highly recommended
Cotton swabs, wooden or paper wound (Q-tips or equivalent)

::::::for the mirror::::::
Cotton wadding or cotton balls
SuperLube or Lubriplate, silicone grease would also work
Lint roller, the tear-off kind
Small set of allen wrenches, fractional sizes for older scopes, newer ones might also use metric
Needle nose pliers
Pinwrench/retaining ring wrench or homemade substitute from PVC pipe - - - be prepared to make this tool,
You will NOT be able to disassemble the mirror and carrier assembly without some way of removing the retaining ring

It might seem somewhat daunting at first, but it really isn't too difficult and is a simple one or two day project.

Get the ROR and put some in a dropper bottle. Use a drop of that and a cotton swab (Q-tip) to clean gunk off eyepieces,
like mascara or fingerprints at a public stargaze.

CYA stuff:
This is how I do it and I achieve good results. Your mileage may vary. If you break your mirror you get to keep both pieces. If you are apprehensive about doing this, then.....DON'T.