Very few pilots actually own their own aeroplane, and even less have a private airstrip. Most pilots hire their aircraft. Even if the aircraft is owned by the pilot, that pilot will usually interact with several airport staff prior to taking off - any one of whom would take action if they suspected he was drunk. I would not like to land an aircraft after a couple of pints though. Even then, the most likely outcome would be a bent aeroplane rather than any serious injuries if the pilot is experienced, and even if there is a bad accident, there is relatively small danger to people outside the aircraft.
Pilots usually have to regularly report by radio to air traffic control.
If ATC detect something wrong in how the pilot sounds or responds, they will alert staff at the destination airport. The prime reason is not because drunkenness would be considered likely, but that a medical or environmental problems may be suspected. Carbon monoxide in the cockpit, anoxia from flying too high, hypothermia are all possible concerns that ATC staff would have apart from deliberate intoxication if the pilot appears disoriented and has slurred speech. The recent publicity over the drinking habits of commercial pilots aside, there are no significant numbers of aircraft accidents where alcohol played any role whatsoever, even though there are certainly many pilots who are regular heavy drinkers. All accident reports are available on the AAIB website, which I have read every month for about the past 7 years.