*(this will apply to window units as well as full size units, but I will describe only Full size, Split systems)
Hi,
When your A/C is not working, you want it to, right? well first you need to have an idea of what is wrong.
Home a/c units run to remove heat and Humidity from the air inside your house.
to do that there needs to be airflow accross both the outside systen and the inside system. Think of it like this, how hard is it for you to breathe with a bag over your head? OK, now first question, Is your indoor blower running? is there air blowing at all in the house? if not, you could have a thermostat problem, an air filter problem, a blower motor problem, or an electrical problem. you can easilly check the air filter, the other problems may require a technition.
if the air is blowing in the house, lets check outside.
is the fan on the outside portion of the a/c unit working? if not, do you hear noise coming from the unit? if not, you mostlikely have a power problem.
if Both the inside air and the outside air is blowing, but you are not getting cool air, lets go further.
Outside, do you hear both the fan and the compressor running? several things can cause a compressor to fail, overheating due to dirty outside coils, or low freon, and electrical problems.
Next, if you hear both running, but you still are not getting cooling, let's check the lines temperature. where the outside section (condenser) of an a/c system meets the house, you will have two rigid lines, one is larger than the other and it will usually have black rubber insulation on it. this is the line you need to check temperature on. the other small line should be ignored for the most part. gently pull back a small amount of insulation on the large line, and gently, feel the temperature. Caution! if this is a heat pump and there are problems you could seriously burn yourself!  is the line very cold? if so you have a problem inside your house. Very cold large line temps are caused by insufficient heat entering the line.either there is an airflow problem or a low freon problem. you can easilly check the airflow problem, pull the filter and inspect it, or verify the blower is putting out good airflow at your vents. Good airflow and a clean filter means you most likely have low refrigerant condition. Shut off the system and call a tech.

Maintenance:
first your a/c system needs to be working properly to be effectively maintained. see above
now, having cool air and having an efficient a/c system are two differant things.
a simple thing to do is keep the aif filters in your system clean. standard mesh filters need to be changed once a month on average during a/c season to keep your a/c running well. advanced filters can go longer depending on the manufacturers recomendations.
also each spring, before you really need your a/c unit, the outside coil should be cleaned inside and out, of dirt, grass, pet hair, and leaves. the cleaner the outside unit is, the better your system will cool, and the fewer $ you will need to cool your house.
Refrigerant should not be needed in a well maintained a/c system. If your system needs refrigerant on a regular basis, you have a leak. either the unit was not installed properly, or damage has occured causing a leak.  An easy way to check if your freon is correct is feel the large line under the insulation. Caution! if this is a heat pump and there are problems you could seriously burn yourself! If the large line feels cool like a drink container fresh out of the refrigerator, it is pretty close to correct freon level. if it is slightly cool, or VERY cold, you have a freon issue.

remember when you have determined that a service tech needs to come out, tell them what you have found, and TURN OFF the system. if it's not cooling, leaving it running makes it MUCH more difficult ie. expensive to repair.