Cistern Pump Help!

HELP! Our cistern pump is acting up and we have no clue what to do. Sometimes it doesn't want to shut off, even if the PSI is correct, and most of the time, it constantly "spits" the water out of faucets as though there is air on the line.

How do we determine what the problem is on our own w/o paying excessive money for a service call?
THanks for any advice.!