First, you need to check whether there are any signs of life. With your fingernail, gently scrape away at the bark on one of the branches to see if there is any green showing underneath. Try in several places if you have no luck to start with. If there is some green there, then you are in luck and it will probably recover.
The soil may look damp on the surface, but in the middle it is probably as dry as a bone. Get yourself a washing-up bowl and put the tree plus pot in the bowl. Then fill the bowl with cold water so that it completely covers the pot and all the soil. Wait until all the air bubbles stop (it could take several minutes), then take it out, and put it on the draining board until all the excess water has drained out of the hole in the bottom of the pot. There should be a 20p-sized large hole, possibly two, in the base of the pot. That's why bonsai pots have large holes, to let excess water drain out.
Then put it in a light place, out of direct sunlight, draughts, and away from sources of heat like a radiator, and keep your fingers crossed.
If it's a Chinese Elm, then there may still be a chance, and after 2-3 weeks, you could see tiny green shoots start to appear all over. If it is any other variety, it's probably had it. If you do see new growth, then water it again normally and treat as you would a houseplant. You often find that water poured on the top will just run down the sides of the rootball and out of the bottom without actually wetting the soil, so periodically do the washing-up bowl trick just to make sure.