The most people I have seen at my field at a time is about a dozen so flight time isn't too hard to come by. Most of us know each other by name so we usually talk a bit and basically someone calls that they're going up next, and so on. If there are only a few people at the field I wait until a person is landing and then start up my plane so I can taxi out when they are taxiing in.

Lets say a 40 size plane takes up 1 cubic yard (rounding). If the planes are flying out 200 yards, 300 yards along the runway and 100 yards up. Thats a flying area of 6 million cubic yards. So the chance of a midair is 1 in 6,000,000!