I installed new 20 gallon pressure tank today , along with a pressure switch and pressure gauge. I have a one and a half hp. Above ground pump.Now the problem is that the tank will not fill up with water.I installed a tap off the tee and water comes out of that, but it will not go in the tank. Did I do something wrong in my install?

You have a "bladder" in your tank separating the top air cushion from the bottom water resorvoir. Your problem is this: the bottom section is, at present, filled with air. So it tends not to fill completely with water. After a few weeks, the air in that section will be absorbed into the water, and the bottom section will then completely fill with water. Give it some time.

BTW, your question is asked frequently on this board. It is rather common.

The tank should fill up within a few minutes and the switch should shut the pump off as soon as the proper pressure is built up. There are two types of jet pumps also (Shallow Well and Deep Well) The major difference being the size of the VENTURI in the pump. A deep well venturi can work on a shallow well pump but a shallow well venturi will not work on a deep well. An above ground (jet pump) should have either a 20-40 or 30-50 switch. If the pump keeps running but is not shutting of then there is a problem with the well pump trying to prime, the switch or it could be a bad check valve. When you started the new pump up did you pour water into the top of the pump to help it prime and keep it going until the pressure started to build? A jet pump works by creating a vacuum at the top of the drop pipe and pulls water up the pipe. If any air is still trapped in the pump or drop pipe the pump can not build "HEAD PRESSURE" and may run for a very long time but will not shut off.
RJ

Also check the pre-set pressure of the well tank (tank needs to be completely empty). The tank pressure needs to be 2psi below what the CUT-IN pressure for the switch is. If there is too much pressure in the tank it may no fill.
RJ