There are a few different methods for connecting a dishwasher drain, says About.com. The plumbing section of this website describes the details for connecting a dishwasher to a drain pipe.
If the dishwasher drain hose has a large end, it will need to be trimmed to fit the end of the air gap. Connect the dishwasher drain hose to the air gap with a hose clamp and then connect the large end of the air gap to the garbage disposal with a rubber hose. Use hose clamps one both ends of this connection. Straighten out any kinks in the hose that may cause blockage.
To do this without a garbage disposal, the dishwasher air gap must be connected indirectly to the sink drain. In this situation, the large end of the air gap is connected to a y-branch tailpiece with a rubber hose. This tailpiece comes in two sizes, so be sure to measure for the right one. Clamp the hoses in place after straightening any kinks.
For a high loop to disposer connection, one must check local building codes to make sure a high loop connection is allowed. Pull as much drain hose from the dishwasher as possible and use it to make a high loop before attaching it to the garbage disposal. Strap the extra hose as high as possible under the sink.