First you need to determine if the circuit can handle having both a dishwasher and garbage disposal on it. You can check the DW and GD for the actual wattage but in general a DW pulls about 1200 watts and a GD pulls between 500-950 watts. A 15 amp circuit is rated for a maximum of 1800 watts, a 20 amp circuit is rated for a maximum of 2400 watts. Normally a DW and GD are placed on dedicated circuits. You also need to make sure the box can handle the additional wire. Your junction box needs to be able to accommodate 20.25 cubic inches for this application (this assumes 12 gauge wire and one switch). Most single gang boxes are between 18-20 cubic inches.
As far as the wiring (this assumes you can safely run both off the same circuit); run a jumper from the common (black wire) that is supplying power to the switch (you will need to make a pig tail and send one wire back to the switch and tie the other into the DW common). Tie your neutral (white) and ground (bare copper) into the existing neutral and ground pig tails. Make sure you use a crimp on the ground wire pig tail to hold them together. Use red twist caps ( or caps rated for your application, whatever you use they should be capable of handling 3 - 12 gauge wires) for all the other pig tails.
Ultimately if wiring is not your strong suit then I would highly recommend you consult or hire an electrician to do this work. I would also highly recommend running a dedicated circuit for the dishwasher and not tapping into an existing circuit. One additional consideration for you will be what the manufacture calls for as far as wiring; many hardwired appliances call for a dedicated line to supply the appliance, failure to provide such wiring will void the warranty and/or may cause damage to the appliance.
