I've only done one field recording at an airshow so far, but here's what I know from that.
First, check the event website and read the media policy. Are there copyright restrictions? Do you need to register for a media pass?
With military aircraft present security will be tight. However, they should also be used to seeing people with SLR gear so sound recorders shouldn't stand out too much. Expect metal dectors and fenced off areas as you search for a crowd free spot to record.
Get a copy of the schedule, but don't expect things to run on time. Allow for a whole day to record if you can.
Finding a place to record can be tricky. You have three main forces against you. First is the crowds of people making noise. Second is the speakers playing music nearly everywhere. Third is that aircraft are sharing airspace so it can be tricky to find a helicopter flying without a jet being audible in the background.
But good thing is the airshow space is huge, so you just need to find an outer area away from the intersections of aircraft. I found car parks and places and along the long driveway in were both people free and had isolated aircraft flying overhead. Expect to have to walk around a lot to find the best spot.
Onto the actual mics, I just used a shotgun on a boom pole in an attempt to get a directional mic above the noise level of any people. This seemed to work well, but time permitting I would have added a pair of stereo mics to this. The soundwaves bouncing off the ground is what really adds to the power of a jet - but you may need an assistant if you are going to move all this gear around
Obvious thing also if you're following the aircraft with a directional mic you'll aim a bit behind the aircraft, especially for jets. Lastly pre-rec is your friend for when that massive bomber flies low overhead. (Oh well, it sounded amazing so at least I got to hear it if not capture it.) Again obvious, but watch your levels, wear ear protection and record at the highest rate you can do.