How do I test how well capacitors are functioning?

What kind? Flux?

Electrolytic capacitors out of an LCD tv.

Are you trying to characterize them yourself or just trying to see if they are still working capacitors?
Obviously the best way would be to use a multimeter that has a Capacitance scale. The meter drives the cap with a known frequency through a known resistor and looks at the RMS voltage across the cap. If you don’t have that type of meter you will need either an oscilloscope or some frequency generator and resistors. Do you have those?
Is there any way you can read the capacitance values visually? Many caps are labelled.

Capacitors are neat things to have around when you are making electrical projects. If you plan on doing that for fun I’d invest in a $40 meter that has the right scales. It will make life much easier for you.

@LuckyGuy Aren’t you worried about driving an electrolytic with an a/c signal (i.e., incorrect polarity half the time)?

I found the following advice here:
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You can use your multimeter as an ohmmeter to test the capacitor.

1) Discharge the capacitor by [shorting] its leads. That is – use a wire and connect the leads of the capacitor together. This will discharge it.

2) put your multimeter in the high ranges 10K-1M

3)CONNECT MULTIMETER TO CAPACITOR LEADS (OBSERVE THE POLARITY IF ELECTROLYTIC). AT SOON AS THE LEADS MAKE CONTACT, THE METER WILL SWING NEAR ZERO. IT WILL THEN MOVE SLOWLY TOWARD INFINITY. FINALLY THE METER WOULD COME TO BE INFINITE OHMS BECAUSE THE CAPACITOR IS BEING CHARGED BY THE BATTERY OF THE MULTIMETER.

4) IF THE CAPACITOR IS BAD, IT WILL GO TO ZERO OHMS AND REMAIN THERE. THIS IS CALLED A SHORTENED CAPACITOR

5) IN THE CASE OF AN OPEN CAPACITOR THERE WILL BE NO OHMMETER INDICATION.

6) SOME CAPACITORS HAVE A LOW DIELECTRIC LEAKAGE. YOU WILL KNOW THIS IF THE OHMMETER COMES TO REST AT A POINT LOWER THAN INFINITE. TEST A KNOWN GOOD CAPACITOR OF THE SAME TYPE TO BE SURE
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Hope it helps.

@gasman. Nope not worried at all. My tester does not use high voltages. I know it starts putting a 1 kHz signal across the leads and then changes frequency automatically to change range.