OP was asking about air gap, calling it air vent. This confuses some of the answerers. All the above info is correct. What I am about to say here is not a contradiction. "Gap" is before the P trap, on the room air side. "Vent" is after the P trap, on the sewer air side. As for air gaps, they may be overkill. Many think they are. Every dishwasher has a drain hose that either goes up to the air gap, or else it goes up "high" to make a high loop under the counter before going back down to its connection to the plumbing. This hose connection is always somewhere before the P trap, not after the P trap. High loops are fine. Air gaps are more better. Why? For a few reasons that require a large number of words and are best given by an expert on public health and the water system. Even Master Plumbers argue about it a lot. Executive summary: it's nothing to worry about.

Mine comes up behind and in through the diagonal back of the cabinet, in the dead space created in the corner. I'll see if I can dig up a photo from before counter tops went in. Found a photo...you can see I built the corner cabinet 28" deep, which allows nice room behind the sink for all the hookups. New sink is single basin, so I since covered the extra hole in the cabinet back where the old waste was from our double bowl. This post was edited by ctycdm on Thu, Oct 9, 14 at 11:06

That's unfortunate. Are you familiar with Murphy' Law? Well, what can go wrong, will, and did in your case. There are some things that can easily be accomplished, however, gaining significant storage will require more extensive measures. You can move the recep. box mounted on the floor of the cabinet, to the wall, however, if there is an additional feed from that box, through the floor of the cabinet, it becomes more difficult. If you opt to eliminate the switch/s/ and install an air-switch for the disposal, than have 2, 20amp recep., 1 for the DW and the other for the disposal. Feeding the DW off of a recp. is fairly common, however, I'd relocate the place the cord comes into the cabinet to the lower rear corner. There are two option for the placement of the air-switch, switch. Either drilling the counter or installing it in the cabinet face frame. The disposal uses the high loop instead of an air gap, however, the hose can be shortened and connected. You may feel that the disposal is the problem, when it's actually the 2" waste line and where it penetrates the cabinet and the loop vent does not help. It should have been contained within the wall. Both methods of correcting that would require removing a portion of the cabinet floor.

Actual plumbers, and not "drain cleaners" do know plumbing code and how to properly vent things. You don't need an architect or an engineer for most residential plumbing work. You do need someone who knows code - at minimum. I've been the GC on a ton of residential gut jobs and never needed an engineer or architect - but I did need good trades people. Again, you came here wasting everyone's time with an unintelligible question and nothing specific like a diagram. You got exactly the right answer - the first one right out of the gate. And then you want to insult us and be an ass. Good luck with your plumbing job - because nobody wants to deal with your nonsense and your attitude.