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.
PS: This test works for large capacitors. 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.