I'd just leave it alone. Anything more than blowing the dust off it will likely ruin it. Taking it out to clean it will just allow dust into the pentaprism, could make things worse in the long run.
I have done such forbidden stuff for years. I would do the following: remove the screen and hold it by the sides. (Have a very soft camel's hair brush handy.)
Now go to the kitchen sink and squirt a drop of dish liquid on the screen. Then wet the brush and brush the screen on both sides. Rinse the screen WELL and then, finally, dip it in an ounce of clean water that has a drop of wetting agent in it. Then use a hair dryer to dry each side of the screen.
The dust can also be on the underside of the prism. Before placing the screen back blow heavily on the bottom of the prism (but make sure that your lips are VERY dry so no saliva goes with your breath!) If dust is still on the mirror use a VERY clean DRY camels hair brush to brush it clean. I have even CAREFULLY cleaned the bottom of the prism with a tiny, clean tissue with a drop of Windex. (Watch not to touch the damn black baffle that prevents the mirror from banging up to hard. That black stuff is sticky and can cause all sorts for problems, especially if some gets on the screen.) This all is not a big problem if you are careful not to scratch the screen. The screen is very vulnerable to scratches because it is soft plastic, but what I have said works and will cause no problems. - David Lyga
I've clean non-removable focusing screen with q-tips dipped in alcohol. If you're real gentle, they won't leave behind lint, at least the ones I use didnt.
Since FM3A has a removable focusing screen, you can remove it, and brush off dust with gentle brush and puff of air. I really wouldn't do anything more.... You CAN wash it with distilled water but dust will get on it during drying process.
I've tried cleaning mine on trashed camera once. That thing is alot softer than I imagined and I am certain the result wasn't any better than when I started.
Well,the O.P. will be well confused by now. His user manual will describe how to remove/replace the focus screen.
David has the gist of it ,but I 'll repeat : the Thomas Tomosy method,which has the additional benefit of actually working,should replace most of the dubious advice offered so far.
Dilute a little dishwash detergent in warm water. Plunge the screen into this.
Use a very clean,soft brush to brush both sides. Remove screen, rinse in clean water. BLOW DRY - DO NOT WIPE - with anything -no tissue,no Q-tips,Nada.
Lean on tissue to air-dry.
Works on ground glass,acrylic,anything.
One last tip - if the crud is out of focus,but still visible -it is probably on the screen side of the prism. Best method is a small blob of -here it's called Blu-Tak, held in a fine pair of tweezers -it will lift the specks without marring the glass surface.
Now, can we have another thread about how impossible it is to clean a front-silvered mirror ?
But, my variation is a last wash in *very* dilute dishwash detergent (or Photoflo) solution, say about one drop a litre...
Also, while good for single-layer screens like the OP's, it shouildn't be used on compound screens which are combined with a condensor (at least, without dismanteling them - Nikon F/F2, for example).
Mirrors: the drastic solution is supposed to be to brush on a collodial solution, let dry and peel off...
NOTE!!! I haven't actually tried this (yet - mainly due to difficulty finding collodial solution). YMMV!!! Try on a junk camera first - I warned you!!
Now how about a thread now on the "extreme difficulty" of finding substitutes for mercury cells? ;)