Electrolytics larger than 1 or 2 MFD should cause the meter to deflect all the way to zero, set at the 10,000 ohm setting. Then the needle should fall back all the way to infinity. If, after a while, the needle does not fall back all the way, then the electrolytic is either leaky and bad or it needs to be rejuvenated. To rejuvenate, attach the condenser to a DC source that supplies the rated working voltage listed on the condenser (375 volt condenser should be put on a 375 volt source). Connect a 5K ohm resistor in series. Power it up slowly and allow to run at full voltage for 20 minutes. If the resistor starts to smoke, then the condenser is likely shorted, and should be replaced. If the condenser gets hot, this is also a sign of a short. The condenser should not get hot. This is dangerous, as steam pressure could explode it. If, after 20 minutes, nothing has smoked, and the voltage at the condenser is where it should be, then turn off the power and carefully disconnect the condenser. Connect a 30K resistor across the condenser and allow it to slowly discharge. Retest the condenser. If the needle will not fall above 10meg, then the condenser is leaky. Leaky condensers are not good. Generally 1 meg resistance or higher is acceptable, but I do not like to use electrolytics with a leakage resistance less than 10meg.
As for testing paper and mica (and other materials) non-polarized condensers, use the same setting on your meter. With condensers smaller than .001 MFD, you will not likely see a deflection at all. When connecting your meter, watch the needle closely, and as said before, DO NOT touch both leads at the same time. When the meter is connected, the needle will swing up just a small amount. Then it will fall back down. It MUST fall right back to where it started (the infinity mark). Any leakage at all is NOT ACCEPTABLE. If a condenser smaller than .001 MFD is tested, and the needle swings up, make sure it falls back down. Any condenser with leakage will cause the needle to swing up even if it normally wouldn't, so pay close attention. Leakage in the 10s of millions of ohms does not usually cause equipment damage, but tubes operate under extremely sensitive high impedance conditions. 10 meg leakage is just enough to pass some of the high voltage B+ from one stage to the grid of the successive stage. This positive voltage will throw off the slightly negative grid voltage of the succeeding stage, and cause distortion in the audio as well as inefficient amplification.
Thomas
When I pull out old caps, I do kind of like to know how bad they were, just out of curiosity. For paper caps, I test them with my Fluke DMM's capacitance mode. If the old cap measures high, maybe 2x its rated value, then it's a good sign that the cap was leaking significantly.
I also check the value of the new, replacement cap to make sure I didn't grab the wrong value, etc.