Well Pump Doesn't Shut Off
You check the pressure with a pressure gauge which should be attached (permanently) to your system near the pressure tank. If you need a quick and dirty check, you can get a pressure gauge attached to a garden hose fitting and attach it to a hose fitting, but the standard pressure tank Tee has a port for the pressure switch and a port for the pressure gauge, right there, and one should be there at all times.

There is no single "correct pressure" - there are some standard or typical pressure ranges for well-pump systems, and since the usual non-adjutable differential is 20 PSI, those are 20-40, 30-50, 40-60 and 60-80 (no reason you could not use 50-70 or 35-55, just not typical enough to see numbers quoted for them.) Many folks consider 20 PSI rather low, and many fixtures don't like an inlet pressure above 80 PSI.

Without knowing what your pressures are, it's hard to say if the well or pump is failed and the pump can't get to shutoff pressure, or if the pressure switch is failed and not cutting off.