there are quite a few different methods to cleaning dirty coins doing a google search for cleaning ancient roman coins you should find some info.
if it is a coin you really dont want to damage the coin the safest (also the slowest) would be distilled water , place the coins in a cup with the water for 3 days then change water an do again until finished. the theory is the water has had the minerals removed from it so it is starving for minerals and that is what is stuck to the coin ,so the water slowly eats it off , but you must use new water every few days as the water absorbs the minerals it will become saturated and no longer need the minerals. this method does work very well but does take a long time
if you want to blast the crudd off then try electrolisis but be warned this can damage a rare coin , it usualy darkens the patina.
i use a 9v adapter that plugs in the wall and connect alligator clips to each wire i then get a bowl of salt water (the amount of salt will have an impact on the process ) and a piece of stainless steel .
attach 1 clip to the coin and one to the stainless put the coin in the salt water and insert half of your stainless(spoon fork etc.) into the salt water about an inch from the coin making sure this clip is attached to the spoon above water ,if the coin is fizzing then you have the + and - wires hooked up right if the stainless is fizzing then switch the wires! your stainless will get severly pitted with this method so use scrap , i shear strips at work about the 1 inch x 4 x 1/16 . in no time this will get most dirt off anything but may harm whatever your are trying to clean!
there are many other methods out there , olive oil soak, glue gun the coin dry and peel (does sometimes work real well) rapid freeze to heat ( coin expands at different rate then dirt thus cracking dirt) and so on but the 2 above i use and have worked for me