If the reels and the film on those spools of film are dirty, don't unroll them until you have cleaned them.
The film in the middle may still be nice and clean. Unrolling film from dirty reels might spread the dirt around to parts that weren't dirty in the first place and make a bigger mess than you started with.

Take the film outside to a sheltered area such as a garage and carefully clean the outer parts of the reels with a chamois or something similar.
I've seen people use air nozzles to blow dust and dirt away but I don't care for that for several reasons. I suppose canned air might work for small jobs.

If you can remove the reel flanges from the rolls and work with bare spools of film, that would be better. Rusty, dirty reels will only serve to spread dirt.
You should probably get new, non-metallic reels.

Unspool the film carefully, keeping even tension. Use a pair of spindles if you have them. Even tension and smooth winding are key.

Other than that, cleaning movie film and cleaning still photography film are very similar in terms of chemicals and materials. Only the technique is slightly different.
The typical method is to use a dust free cloth (or better, a Kimwipe) and fold it over the film and wipe as you SLOWLY spool the film from spindle to spindle. There are two things to watch out for: Too much winding speed and dirt build up on the cloth.

Remember, as the film winds from reel to reel, the speed changes. The payout reel gets smaller and smaller. The take-up reel gets larger and larger. The change in diameter will cause the film to go faster and faster as you get toward the end of the reel. Greater speed means greater chances for abrasion and film damage. Also, the tension on the film will increase. If it gets to high, your film could break.

Just wind the film slowly and regulate your speed throughout the operation. When I do 35mm film, I never go faster than half speed. Often, I don't even go above 1/3 or 1/4 speed.

The other thing to remember is that dirt will build up on your cleaning cloth. Dirt on your cloth basically turns it into sandpaper. Change your cleaning cloth often to prevent abrasion from dirt.
I fold my cleaning cloth in quarters then double that in half to fold it over the film, cleaning both sides simultaneously. Every once in a while, I stop and refold the cloth so a clean side is facing out.
(Folding in quarters then doubling over again gives you eight uses out of one cloth if you do it right.)

Other than that, it's all pretty much the same as working with still photo film: Work slowly, take your time, keep things clean and pay attention so you don't scratch film. 90% common sense, really.