Examine the outside of the well cover, making notes of any bolts or valves that attach to the cover from below. There's usually a minimum of four bolts holding the cover down, as well as valves for the intake of water.
Remove any fittings that attach the valves to the well cover. If you try to remove the cover without first taking off the fittings, the cover will only move a few inches, and not come off completely.
Loosen the bolts holding down the well cover and try lifting it slightly. If the well cover comes off completely, you're in the clear. The bolts attach the well cover to a metal plate below and if it doesn't come off easily, you need to loosen the bolts more.
Lift the well cover again and look for any signs of resistance. If the cover doesn't come off easily, you'll need to look for anything else that needs removing. The valves or pipes extending from the well may need to come off.
Take off the well cover by lifting it directly off the top of the well. If the concrete cover is fairly heavy, you may need to find some people willing to help. Simply pull off the concrete well cover and move it to an area near the well for easy access later.