First all of you have to see whether it is polar capacitor or a non-polar one. If it is in cylindrical shape then it is a polar capacitor. You should search for the images of such capacitors online for more clarity.
Now you must know the working of the capacitor first- it is basically two conductors isolated from each other having a non-conductive medium in between. The charge accumulates at the conducting surface of capacitors. Positive charge at one side and negative on other side.
1. In case a capacitor is not working then it means that somehow the capacitors have short circuited. For this you need to see the resistance between the two pins of the capacitor. Set the multimeter to resistance, now connect the wires of the multimeter on the two pins and see the resistance. If they are short circuited then the value shown will be 0. Many multimeters also make a beep sound to indicate shorting. If they are short then they are not working.
2. It is also possible that they are showing infinite resistance initially whereas they should allow at least some current to flow while the capacitor plates charge. This case is too of a faulty capacitor. Make sure capacitor is initially discharged by connecting the pins to ground and then connecting the pins. The resistance should go from some value to infinity otherwise it is faulty.
However, please note that you can't do these tests while the capacitor is connected in circuit because there might be parallel connections which will make provide an alternate circuit path making the test void.