Step by step.
1. determine if you have a captive bladder tank - they have the shrader valve t apply air on the top of the tank.
2. Check what the cutin/out pressures are (they should be 20psi apart, e.g, 30-50 or 40-60). Done by watching the gauge as pump runs/shuts off. Now check the pre-charge with the tank empty, or empty as far as it is possible. Turn off power and open a drain valve at the lowest point in the system and anothe one higher up to allow air in (tank won't drain well without that). Check air pressure: As someone else said needs to be 2 psi below cut-in pressure.
If teh pump cycles but the differenttial between cut/out is significantly other than 20psi you need to adjust the pressure switch (or replace it, cheap part, quick replacement and it will already be set for either 30-50 or 40-60)
3. close valves and turn power back on. Watch the gauge it should show a slow climb until it shuts off. Probably take a couple minutes if you have a fair size tank.
4. If pump doesn't shut off you have either a bad pump or well is running out of water. BUT there is an odd problem than can cause it. Plugged up little bitty riser pipe the pressure switch sets on. Happened to me. Pull the switch, pull the pipe and ream it out. I had to use a drill bit. Symptom of that is pressure very slow to build up and then going to overpressure and pressure dropping to very low before pump starting.
A sparepressure switch is a nice thing to have in the middle of a blizzard. Ask how I know.
Harry K