Measuring Capacitance and ESR

Measuring capacitors is tricky because it doesn't "flow" power like other devices. Their capacitance can only be measured while charging or discharging. Most multimeters are not capable of doing this kind of measurement. LCR meters are typically used to do this and there are inexpensive models available making this viable for enthusiasts as well. LCR meters are capable of measuring the capacitance and the ESR of a capacitor which. Comparing these to the rated or expected values can give you an idea if a capacitor is bad.

ESR meters may claim to be able to measure a capacitor on a circuit board but other parts connected to the same board can affect the readings you get. There may be many capacitors near RAM chips and all connecting the power rails to ground for decoupling. These will be parallel to each other in circuit and will change the measurement. You can disconnect one side of a capacitor to get a reading while on a board but personally I would just remove it to avoid fatiguing the copper pads on the PCB.

Multimeters aren't completely useless for capacitor testing, but they can really only be used to test for shorts using the continuity test. At least that's a pass fail test, if it's shorted, it's very dead. And that can usually be done on the PCB as well.

Taking your measurements and using them to determine the condition of a capacitor will require understanding what they mean and having an idea of what "normal" is. Lets go over some info on capacitance and ESR to understand how they may change:

Capacitance
When you measure the capacitance of a part you may get a value different from what it is rated for. The tolerances on consumer grade capacitors can be fairly high at 20%. So you need to check what the +-% rating for a capacitor is before making a judgement. Capacitance will only go down on capacitors, if they are reading below the rated value minus the tolerance you can pretty safely assume it is bad.

ESR
ESR is lower is better. There is no magic number for what "correct" ESR is because it's a rated value for them. The value should be less than a kilo-ohm, and depending on the quality of the capacitor should probably be less than 100ohms. Identifying the type of capacitor and finding new examples with similar ratings online to compare to will be a helpful option here. Looking at similar capacitors from Digkey, Mouser, etc and seeing what values the manufacturers rate them for can give you an idea of what "normal" is.