If the AC compressor doesn’t turn on, the most common culprit by far is low AC refrigerant. If there is a leak, no matter how small, it’ll eventually cause a non-working AC system. Another possible issue is a blown fuse and/or relay. Your owner’s manual should be able to tell you where those are located. Poor grounding, frayed wiring, bad clutch coil, and defective AC pressure sensor switch can also be an issue although less common.
After testing the AC for the amount of PSI in both low and high-pressure lines, re-fill the AC and monitor the gauges carefully. Some AC refrigerants already come with the gauges built-in.
If you suspect there is a leak when re-filling the AC refrigerant, a dye can be used so that next time it stops working, the dye will be visible when you check it in the dark with a UV light.
Any leaks will glow in the dark (greenish-glow). I would recommend starting at the A/C compressor and going along the A/C lines inspecting all areas carefully.