How to remove keyboard grease?

Diluted Isopropyl alcohol on a cloth is the best for removing oils and grease. Try to buy it pre-diluted or dilute it yourself using demineralised water. Never use it non-diluted as the alcohol can damage the plastic. 50% is probably the maximum safe mix, 30% Isopropyl alcohol or less on more sensitive surfaces.

Don't use a dishwasher unless you're prepared to lose the keyboard. Every model is different and some have exposed electircal surfaces that if not dried perfectly will short circuit the keyboard.

The easiest way is to run it in the dishwasher.

There's a YouTube video demonstrating this:

Even Jeff Atwood mentions it:

The video shows the keyboard going in whole - I remove the keys first and put them in the little things holder in our dishwasher - this helps the drying time.