You need a DC voltmeter--which will probably be part of a multimeter including AC and DC volts, Amperes to about 10 amps, several Ohms ranges, perhaps capacitance, perhaps a "battery testing" (AAA, AA, C, D, 9-volt) set of ranges which puts a small load on the battery when testing it's voltage, that sort of thing. Features vary with the meter selected. There's a million choices, and almost all of them are going to be cheap Chinese even if they're not inexpensive.
You will need either fine-wire "back probes", or a "test harness" that you can pierce the insulation and not damage the actual vehicle harness. The "back probes" may or may not be included with the meter you buy.
You'll turn the meter on, and select a DC voltage range that's as low as it goes and still accommodates 15 volts. On MY meter, that's the 40-volt scale, but other meters might have a lower voltage range--20 or 24, perhaps. A 6-volt scale won't accommodate 15 volts, so that's too low.
Testing the power supply TO the pump will require grounding the black meter probe, (preferably at the negative battery terminal, using a length of ordinary primary wire as needed) while sliding the red back-probe pin into the connector, past the silicone-rubber seal, so that the back-probe contacts the metal pins of the connector, and the meter is connected to the back-probe pin(s). You'd probably run the engine at this point, so that the pump is running, and you'd read the voltage on the meter. The alternator is likely charging at 14+ volts, so you'd better have 12.0 volts or more, showing on the meter. Remember, you're not testing the harness between your test point and the actual pump--the harness going up and over the tank, and the in-tank harness. A problem there is "invisible". But this is the best you can do without damaging the vehicle harness or dropping the tank/lifting the bed.
When testing the ground side, you'd do essentially the same thing. Ground the negative lead. Touch the red probe to the ground wire conductor as close to the pump as you can reach. This will require piercing the insulation of that wire, and you'll have to "patch" the insulation with something--"liquid electrical tape", real electrical tape, a dot of RTV silicone, etc. You're looking for the lowest value--under one volt, less is better.