The disposal goes on the sink opposite of the drain however before you begin you will need a different type of end waste kit to install the disposal.
A conventional End Waste Kit has a Tee that is fitted under one sink with a cross tube to the drain on the opposite sink. On the input end of the cross tube it has a preformed 1/4 bend (90 deg elbow) which turns the end of the tube up to connect to the sink tailpiece.
Disposals come with a 1/4bend packed in the disposal kit. When installing a disposal on a single sink the factory supplied 1/4 bend would be connected to the disposal body then to the P-trap. If you use that 1/4bend, then connect it to a conventional cross tube the cross tube is dropped down about 4" and in most instances this will place the P-trap too low to properly connect to the waste arm coming out of the wall.
The solution is to get a "Disposal Type End waste Kit" which is available at any local hardware or home supply store. The Disposal type end waste kit has a straight cross tube with a flange on the input end. You discard the 1/4bend that comes packed with your disposal and connect the straight cross tube directly to the disposal body. This will keep the cross tube at the same level as the disposal discharge port. Once it is connected to the Tee you will have no problem connecting a P-trap from the tailpiece of the tee to the waste arm. (See illustration below)