You should install the pressure switch. You can't see pressure. You can't set your pressure switch without it. You can connect it to a tee at the pressure switch, or a convenient plug somewhere on the discharge side of the pump if you DON'T have a check valve between the pump and the pressure switch.
You are trying to find out if there is power at the motor or pressure switch. A multimeter is a combination voltmeter and ohm meter. You can buy one at Radio Shack or Sears for $20 (less if on sale), or a more expensive one at H Depot. Get an inexpensive digital meter; fancy you don't need.
Every homeowner shoud own a multimeter and know how to use it. You can't see electrons or Volts. You will use it to check switches and outlets and bulbs and appliances that aren't working.
It comes with two wires, called "leads". You set the meter for AC Volts at a number higher than 240 volts; touch the leads to the contacts of the pressure switch, and read the volts. If there is voltage at the wire from the pressure switch to the pump, and the pump doesn't run, there is a problem with the motor or connection at the pump.
The reset, if there is one, will be a button at the end of the motor away from the pump end. There is USUALLY no reset button on a pump. They usually contain a self-resetting overload switch.
Now if the pump isn't running, you will use the ohm-meter function of your multi-meter. Ohms are units of "resistance" of a wire or other conductor. Small, long wires have high resistance, and short fat wires have low resistance. Very high resistance (infinity, or off the scale) is usually called and "open circuit". Very low resistance is called a "short circuit" or just a "short".
TURN OFF THE CIRCUIT BREAKER. Set the meter to Ohms, or sometimes kOhms, at the lowest value. Touch the leads together and you should read 0.0 or something like that. Now touch both leads to the pressure switch contacts corresponding to the wires that go to the pump. You should read a low value, on the order of probably 10 or 20 ohms. If the meter is set at kOhms, you will read 0.01 or 0.02 or some such. If it reads a high number, or is flashing like it is with the leads not touching, then the motor has an "open circuit"; (no connection). There are several reasons but with your experience we will leave that 'til later.
The vacuum gauge is a special pressure gauge that measures vacuum on the suction side of the pump. It measure in "Inches of mercury"; (In Hg, which is the symbol for mercury. Mercury is 13.6 times as dense as water, so 1" Hg = 13.6" of water which is 1.13 ft of water. You may find one that reads in psi vacuum, but that would be unusual. The 60 psi part of the scale is not useful to you but is there so you don't wreck the gauge when the pump shuts off and you get tank pressure against the foot valve. If you don't have a foot valve, but have a check valve on the discharge side of the pump, then you can use a gauge that measure only 0 to 30" Hg.
The vacuum gauge will tell you if the water is too low in the well but only when the pump is pumping. A shallow well jet pump applies a vacuum to the line to lift the water and to make up for friction losses in the suction pipe. Shallow well jet pumps are usually rated for no more than 25 ft of lift, so if the gauge reads more than 22" Hg you are at the limit of the pump. It might do a bit more but will be very unreliable. You might have to find a vacuum gauge at a plumging supply or at some place like Grainger.
To set the pressure switch, there is usually a large nut or screw on a spring column, and a smaller one below and beside it. To lower the pressure, turn that large on counterclockwise (back off). That will reduce both the start and shutoff pressure. Turning the other one counterclockwise reduces the shutoff pressure only.
You need a place to prime the pump and let water go to waste at low pressure so you can get it running. That should be a valve or plug on a tee at the discharge of the pump.
Start with the multimeter, and installing the pressure gauge that you have.