I just used soap and warm water. I left it for a day in a pot on the counter, and stirred it with a chopstick everytime I went past. It worked well, and all the dirt came off when I cleaned it with a hand-towel. You can try that for starters, and upgrade to other methods if it fails you.
I would also like to note that it's relatively trivial to pull the keytops off it has a two piece design. If it's one-piece, or you want both parts of the key (or want to clean enter, shift, etc) you'll need something to pull it out with. I just used my fingers, and a steady hand. you could use your hands or maybe your boyfriend in a pinch.
What's the date/serial number (an the back) is it a blue logo? Silver?
Taking apart the 1391401 is pretty easy, but you need a thinwall 5.5mm socket driver (whatever they're called) to get at all the screws.