Dishwasher drain water backing up into your sink is indicative of a clog. Generally these types of clogs are right at the outlet of the garbage disposal. Run some water in the sink and turn on the garbage disposal. With water running, dump about a cup of ice into the disposal. The ice chips will help scour out the disposal and the blades. If this doesnt solve the problem then the clog is on down the line and will most likely need to be professionally augered out.
Good luck