Air in the lines of your water well system can appear due to a variety of causes, ranging from simple and easy to fix to "better call a professional" in nature. However, there's no sense in leaping directly into panic mode just because your water faucet spits air. The first step is to conduct a bit of troubleshooting, because there's a decent chance you might be able to track down the issue and fix it yourself. The worst case would be a dry well, but even that isn't an automatic doomsday scenario.
When air finds its way into your water well system, it normally isn't from a leak in the line where water spews out. In that case, the force of the water's outflow usually won't allow air to get inside. However, there are two valves at the pump itself, the check valve and foot valve, that might be loose and sucking in outside air. Make sure they are at least hand-tight and don't have a noticeable intake. You can proceed to other troubleshooting steps, but if the source of the trouble remains elusive, it might be worthwhile to have a professional recheck the valves.
If the below-groundwater field where your pump draws water recedes, the result is air in the line. Too much demand on the aquifer could be the cause, but the solution might be as simple as adding a few more feet of length to the pipe running from the pump to the water below. There is always a chance that a catastrophic water recession might require an entire retooling of the retrieval system, but this is rare. Still, you probably will want to hire a well system professional to extend the reach of your line.
The source of air in your system is sometimes the hot water heater. The simple act of heating water can cause small pockets of air to erupt in various locations, though in most cases these pockets will rise to the surface and be driven out in advance of the hot water flow. That's why a hot water faucet sometimes gurgles for a moment before delivering a steady stream of water. Although you might think this is air in your well water lines, it actually is only sitting on the surface of the water in your heater tank.
A basic understanding of how a well water system works should simplify the amount of necessary troubleshooting in the event air sneaks in. Remember that in order to deliver water efficiently to your house, the system must be closed and free of air. For air to make its way inside requires either a crack somewhere, a loose valve or intake from a source such as the aquifer. Focusing your efforts on the obvious weak points allows you to pinpoint the problem more quickly.