I managed to remove a key (the little white square bit that goes up and down in the hole), but it was difficult. There were tabs on all four sides that had to be pushed inwards at the same time, which is nearly impossible unless you've got four hands.
After prising off the key top, I used two small flat bladed screwdrivers to push in two tabs at once on adjacent sides, and pointy nosed pliers to pull up one corner so they didn't pop back down again while I did the other two.
I found that the sides of this square piece were coated in red sticky stuff, soft drink or something. I cleaned it off, and also the edges of the hole, and it was fine when I put it all back.
For the second sticky key I fixed, I didn't bother pulling the white bit out. I just pulled off the key top then wiped around the exposed part of the white square with a cotton bud dipped in soapy water. Then I pressed it down a few times and repeated till it was moving without sticking.
Washing the keyboard probably would have fixed it too, by dissolving the stuff out, but I've heard of keyboards not working after that, even though they're supposed to be waterproof.