ive cleaned my keyboard a thousand ways:
you can use alcoholic swabs to wipe off the grime (very effective)
you can take a tooth brush lightly dip it in water or windex and brush away
you can flip it over, and vacum it
you can open it take the top and put it into the sink under hot water, use dish washing soap and a brush with long bristles (favorable) to scrub it FYI: some keyboards arent too durable, so the writing on the keys might get erased even by rubbing the alcohol swab on the keys.