Note the turn-on (cut-in) pressure where your pump turns on.
Turn off the pump. Drain the water and sediment from the drain valve at the tank.
Note the air pressure. The air precharge is always measured and set when the water pressure is zero.
If your pump is submersible (down the well), set the air pressure to 2 psi below the cut-in pressure. If your pump is a jet pump (above ground), set the air to about 4 or 5 psi below cut-in. Jet pumps take a while to get really pumping.
There are more complex tests, but that should be a good way to proceed.
Also note that a tank empty of water is much lighter than one that has water. If you drain the tank, and it is still heavy, it is bad.
If you will keep the existing tank in service, flush it. Annually is usually a good idea.
Precharged Pressure tank flush:
1. Connect a hose to the sediment drain valve, and run that to where you plan to drain the water. I suggest filtering the output through a cloth if you suspect the sediment may include sand.
2. Turn off the pump.
3. Open the drain valve, and let it drain until the water stops. It would be possibly interesting to watch the first water that comes out.
4. Close the valve, and turn the pump back on, and let pressure build.
5. Repeat steps 2, 3 and 4 as needed.