Usually there is no real cabinet built ,but for your sake you only need 2 sides, a back and a top.Probably some painted 3/4 plywood. Make sure the "new" dishwasher works before you go through all this trouble. Take it outside and run it through some cycles.A couple of cheap fittings at your local box store will work then hook it to the hose.Let the drain run on the ground.If all is good then measure your diswasher. 24 inches wide x 24 inches deep is the common measurement.
Good luck and say goodbuy to dishpan hands!