Wow, I've never really thought about that until now. I don't think it's possible to use a multimeter. The first way that comes to my mind is put it into a RC network, and calculate how long after charging fully it should discharge to 37% of its final value.
You can use your multimeter as an ohmmeter to test the capacitor.
1) Discharge the capacitor by shortening 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
Vincin's method will work with sufficiently large capacitor values. (Especially if one uses an analog meter.) Tiny capacitors can only be checked with a capacitance meter, or by using them in an AC circuit and checking for variation from calculated voltage drop.
Adding to what Vincin said: Reverse the leads and look for a major kick in the needle. If the cap charged from the DC voltage induced by the meter, the cap will discharge when the leads are reversed, causing a twitch in the needle.
To effectively test acapacitor one should use capacitance meter -one that reads in uF nF pF, an ESR meter is very useful for checking electrolytics in circuit, they are cases where the uF was good on acapacitance meter but cap had high ESR as shown on an ESR one. The point is one meter may not adequately serve all your needs.