Unscrew any casters off of the portable dishwasher with a screwdriver. Empty the space under your kitchen sink and slide the dishwasher into the space so it's close to the sink.
Turn off the hot water valve under the sink and connect a self-piercing tap valve to the hot water line. It connects directly above the water valve and secures with clamps and screws. Twist the handle on the tap valve so it pieces the hot water line. Connect the flexible water line from the water inlet valve on the portable dishwasher to the other end of the tap valve. Secure the fittings with a wrench.
Remove a section of piping from under the sink drain with a saw. The piping is usually PVC so cutting it isn't challenging. Replace the removed section with a PVC coupler. Secure it by using cement primer on the outside of the pipe and the inside of the coupling. Once you're sure the PVC coupling fits properly, apply the PVC solvent to both the coupling and the pipe and twist the coupling on over the piping. The solvent acts as a chemical weld, melting the two PVC pieces slightly into each other to form one piece and create a tight seal.
Attach the drain line from the dishwasher to a pipe adapter, then connect the adapter to the coupler.
Plug the dishwasher into a power outlet to complete the installation. Turn the hot water valve back on and test the system to make sure it works properly.