Rhonda, the pump makes pressure, the tank just stores it. The tank (probably) has a rubber bladder that has air on one side, and water on the other. When the pump runs, water under pressure from the pump pushes against the rubber bladder and compresses the air in there - storing water. If that bladder is broken, the tank will fill with water. Since water doesn't compress, and the pump comes on, it will almost instantly detect that the pressure is sufficient and it will shut off. This constant on/off will ruin the pump and wear on the control box's contacts as well.
So, you need to get a tire air pressure gauge and check the bladder (pressure) tank. As noted, to do this and set it properly, the pump must be off, and you need to open up a faucet or valve until no water runs (this will remove any pressure on the water, and you can check the pressure in what amounts to a balloon of air in the tank). If that pressure is too high, or too low, you'll have problems. If the bladder is broken (i.e., the tank is full of water or if you notice you get water out of the valve when you go to try to check the air pressure), the tank needs to be replaced. If the air pressure is too low, you need to pump some in with a compressor or bicycle pump (it could take awhile - you need a fair amount of air in there!). If someone put too much air in there, the pump won' tbe able to compress it and there'd be no place for the water to go - the pressure will spike to max almost instantly.
If the tank, pump, and controls are working right, the pump will turn on, push water into the tank, compressing the air, until the pressure reaches the high shut-off pressure. Then the pump will turn off. As you use water, it's the air in the tank that is pushing it out - you're using the stored energy put in there by the pump. When the pressure gets low, the control box turns the pump back on to refill the tank.