I am trying to hook up a dishwasher and washing machine in the same drain under my kitchen sink. There is also a garbage deposal there also. Can anyone show me what is the best approach on this?

You're already in deep doo-doo with your washer. While you could use your disposal for the dishwasher the simple fact that the washer sets higher then the connection you wish to connect to will force you to install a check valve in the washer hose. The set up is farther complicated by the fact that the branch tailpiece,(see image) that you'll be4 discharging into has a smaller opening then the hose forcing you to bush the hose down setting up a backpressure that will either blow out the hose connection or burn out the pump motor. Why not just hang the washer hose over a sink tub and discharge that way. Regards, Tom