Unless you're talking about down the cracks, under the keys, etc you could only reach by disassembly, then about the best thing to clean anything with is a pair of microfibre cloths.
I wrote a train-spotter's guide to cleaning screens on Ask Different - the same applies to any hard surface.
repro from Ask Different: Cleaning my Macbook Pro Retina leaves greasy 'streaks' across the screen ...
Two microfibre cloths, available from any supermarket. Don't get the
'smooth' ones specially for glass, they can be a bit hard on a plastic
screen, get the 'fluffy' ones that make your fingers itch, like
picking up tiny velcro.
One cloth completely wetted in lukewarm water [nothing else], then
squeezed as dry as you possibly can [trick - fold in 4, then roll &
wring. You really want it as dry as possible]. The other cloth
totally dry. If the screen is warm, you may need the first cloth
very slightly wetter - but never anywhere near wet enough to dribble
if squeezed - you really don't want any water that could run down the
screen. The cloths work better when almost dry anyway. If the
screen is cold & also dark, i.e. computer off, you'll also find it
much easier to see when it's clean.
Wipe the damp one gently over the screen, multiple times, turning the
cloth, pay attention to the edges & corners. The trick is gentle
repetition, rather than 'force'. Then, whilst the screen is still
very slightly damp, wipe over again with the dry one, completely
drying the surface.
Smears gone forever… well, until next time ;-)
Please don't be tempted to use any type of domestic cleaner or alcohol. You never know what type of screen coating any given screen
has & some cleaners can irreparably damage the coating layer of some
If you mean down below where you could possibly reach with a cloth or even air-blower, then you can in fact put keyboards in a dish-washer or washing-up bowl, so long as you keep the water cool, use no soap except the simplest of [hand] dishwashing detergent [supermarket cheapest own brand contains little in the way of contaminants, hand softeners etc] and allow a lot of time for natural drying, not using the heated dryer cycle.
I know, it's one of those things that you keep seeing in advice columns, yet never dare test for yourself.
Test on some old keyboard you don't care about & report back afterwards.
[Caveat: this works better on expensive keyboards than cheap ones. Cheap ones sometimes rely on a lubricant to fool you into thinking they work smoothly. After cleaning they will become 'clickier' than when new.]