Our central air unit isn't putting out cold air. I was told it might be the capacitor since we have just come out of a black out. Can anyone tell me how to check for the capacitor?

About the only way for normal people to do this is to substitute a known good capacitor. If you have two units (e.g. upstairs/downstairs), and one still works, you can swap the caps and see if the problem moves to the other unit.

Note a few things:

The capacitors are not "normal" capacitors. They are special AC motor starting capacitors (http://www.capacitor-manufacturer.com/capacitor/CBB65A-1.jpg).
You won't be able to get them at a Radio Shack or similar. Must come from an electrical supply house.
There are lethal voltages present even with the power disconnected.
Be extremely careful working in this area!
If you have a proper capacitor, you do not need to disconnect the old one to test.
Just connect the new one in parallel with the old one. If it works, then you can remove it.

If it is the capacitor, they usually run around $20 or so. Just make sure to get an exact replacement.

I hope this helps,
WallyH

Wally needs help:

(3) If you parallel a shorted capacitor with a known good one, you will still have a short.

Define exact replacement? Best way is e.g. a 10 microfarad (uf) starting capacitor for a 240 V application. Voltages can be higher.

Wally needs help:

(3) If you parallel a shorted capacitor with a known good one, you will still have a short.

Define exact replacement? Best way is e.g. a 10 microfarad (uf) starting capacitor for a 240 V application. Voltages can be higher.
KISS is correct. After all, he is the expert in this area!
If the old cap is shorted (although I think this is rare), then the new cap won't change anything.
Also, higher voltage is okay, but what I meant to say was that if you have a dual cap (for fan and compressor), you'll need the same thing. The problem with higher voltage caps is that they may not physically fit where the old one did.

Thanks to KISS for the clarification.
WallyH

I wouldn`t advise to be switching capactors unless they are exact

My advice still stands. Higher voltage caps are OK, except don't replace a cap rated at 370 V with one rated at 10,000 V.

Worst case: The fan is replaced with a 4 wire, It was a 3 wire, there is a dual cap in the AC, the fan cap is replaced with a single and mounted separately.

<snip>
Note a few things:

The capacitors are not "normal" capacitors. They are special AC motor starting capacitors. You won't be able to get them at a Radio Shack or similar. Must come from an electrical supply house.
There are lethal voltages present even with the power disconnected.
Be extremely careful working in this area!
If you have a proper capacitor, you do not need to disconnect the old one to test.
Just connect the new one in parallel with the old one. If it works, then you can remove it.

<snip>
WallyH

Point 1 - In most recent residential systems it is a RUNNING capacitor which is a different animal than a STARTING capacitor. You must know which one you need. You cannot replace one type with the other.

Point 2 - Run caps usually don't hold a charge as they are in series with a winding. However DON'T count on it. Discharge by shorting the terminals with an old screwdriver. I know, you can ruin a large cap that way, but most residential systems don't have really high horsepower motors with really big caps.

Point 3 was already covered. Replace it to test it. Otherwise you will have to buy or borrow a DMM with capacitance measuring capability to test it. Replace if the reading is 10% or more off from spec. Sometimes you can see that the case is malformed like something exploded inside. That is a dead give away that it's shot.

Aside:

Yea, and caps rated at 10K volts will slowly build up a voltage with nothing attached. That's why you have to place a keeper on them. I know.