Have you looked up 'cleaning mainsprings' or 'servicing mainsprings'?
In short, you anchor the center on a rod, or bolt, and pull it out about 8 or 10 inches at a time, don't bother the innermost coils. Working it over good all the while with machine oil (or WD-40) and various grades of sandpaper, folded to do both sides. Then go to steel wool and finish up with a clean dry cloth.
My starting point for sandpaper, on a really grungy spring, is 150 grit, then use finner grades (220 to 320 to 400 is good) then use steel wool. If the spring is in pretty good shape, you can skip the sandpaper and start with 2-0 steel wool and finish with 4-0. Always wipe it as clean as possible before lubing (a little solvent on the cloth is good) and it only takes a small amount of lube, just enough for a thin coat on the entire surface. Usually 4 or 5 drops of oil will do it.
This sounds like a long process but actual time spent will run from 5 to 15 minutes per spring, dependinh on their condition.
Be checking, all the while, for pitting (from rust) and cracks. Either will nix the spring for future use.