The first thing (which I assume you did already) is to inspect the resistor visually. Look for obvious signs of corrosion and burns from overheating. If you see signs of overheated connectors, replace the blower resistor and its connector. If you want to do a quick test of the blower resistor, you can check the resistance of each of the resistors with a multimeter as follows: set the tool to read ohms (a measurement of resistance) and connect one of its probes to the common output terminal of the resistor. Use the other probe to measure the resistance between the output terminal and each of the resistor’s input terminals. Measure the resistance between one pair of terminals at a time.
Of course, to do this, you need to know which terminal is the common terminal (it’s the one directly feeding the fan motor). And you’ll also need to know which of the other terminals is which speed – you can find this information in an online wiring schematic for your vehicle if you know where to look. AutoZone has some great wiring diagrams, and if you can't find them I have the Haynes manual at home with the diagrams. I can snap a photo and share it if needed.