This happens with my system that is kept near an open window. Dust gets accumulated over a period of 2-3 days beneath the keys, on the keyboard head and on the keys a bit. How do I clean a traditional computer keyboard without pulling out the vacuum cleaner every time to remove dust from even beneath the keys.
You can also wipe it clean with microfiber cloths or similar. In addition you can either use cotton swabs (Q-tips), or some special tool to get inbetween the keys.
One such homemade special tool could be a plastic/butter knife with cloth wrapped tightly around it. This should allow for cleaning of most spaces between keys. Clean for a few minutes, before shifting/moving the cloth (or wringing the cloth).
If needed you could use some electronic cleaner, rubbing alcohol, all purpose cleaner or dishwasher in order to get the really dirty parts clean.
It is actually ok to wash your keyboard in the dishwasher. I would put it on the top rack. I would only be wary of doing this if your keyboard is unusually flimsy or fragile.
After the wash leave it out on a towel for a couple of days, at least 2, to make sure it is completely dry before use.
For a more thorough clean remove the keys first, though this may not be easy and I don't think it is necessary.
Edit: if the keyboard is just dusty and the dust isn't sticking to the keys, compressed air is easy to use and quick, you can buy cans of it at the store or use your own air compressor. It doesn't need to be powerful, just concentrated air flow.