The first step toward installation of your dumbwaiter is to choose the location in which to place it. Access to an electrical outlet is a must. A closet is often a good location, particularly for the upper level in a basement-to-first-floor arrangement. Two closets that are situated one above the other is better yet. You can always construct walls around the aperture, as well, if your desired location is currently in an open room. Measure the dimensions of the hole in the floor to match the specifications provided with your dumbwaiter, and cut it out. Build stud walls for the shaft as necessary, and finish them with drywall.
Install a plywood frame at the top of the shaft and bolt the motor assembly to it. You will likely need to cover up the hole in the floor to be able to do so---some 2-by-4s nailed over the aperture makes a good temporary platform. Similarly, attach the lower frame assembly to the floor on the lower level. If you are doing this in a basement with a concrete floor, you will want to use a hammer drill with a masonry bit for easy drilling. Connect the guide rail between the two assemblies and screw it into place, securing it to both the wall and the upper and lower endpoints. Thread the drive belt through the pulleys on the motor. Install a stop switch at both the top and bottom of the guide rail to make the elevator stop at the desired position. Connect the wires for the switches, and plug the unit in. Finish with drywall and a door, if one does not already exist.