Despite what many HVAC companies say, you really don't need to do much in the way of routine maintenance. The most important thing is to keep the condenser coil (outside) and the evaporator coil (inside the house) clean.
When the coils are blocked by dirt, lint, dog hair or cottonwood fuzz, airflow through the coils is restricted. Less airflow means less heat transfer. Less heat transfer means longer run times and higher electric bills. A dirty condenser raises the condensing temperature and pressure and reduces the system's capacity. If you let it get dirty enough to trip one of the safeties you won't get any cooling until you find the safety, reset it (after cleaning the condenser, of course).
To clean the condenser - start by killing power to the system. Use a shop vac & soft brush to get the loose stuff off the outside of the condenser. Follow up with a leaf blower, blowing in the opposite direction of the condenser fan. Most condensing units built in the last 20 or 30 years have the fan on top pulling air in around the sides and discharging it upward, so you would blow down and out from the center. Finish with a garden hose and spray nozzle in the same direction as your leaf blower. You'll be surprised how much mud you flush out even after the vac and blower.
Inside the house, the evaporator coil is relatively well protected by the air filter so replace the filter regularly. Generally it's best to use the basic, low-cost pleated filter (lower MERV number) unless you know for certain your system is designed for the more restrictive higher MERV filter. Both a dirty filter (in any system), and a high-MERV filter in a system not designed for one, restrict air flow across the evaporator. Low air flow (across the evaporator) reduces system capacity, lengthens run time and cost and can even cause ice to form on the evaporator, blocking even more air. Many evaporator coils are difficult to access for cleaning so it's vital to keep the filter clean.
While you're in the cleaning mood, pop the cover off the lower front of your refrigerator. Lay down on the floor with a flashlight and look at the giant dust bunnie under there. It's hiding the condenser coil. Unplug the fridge and vacuum until you can see all of the condenser coil. It may look something like a black wire basket bent into a deep V shape. There's also a cover on the lower rear of most residential refrigerators. You'll probably need to remove it to reach all the dust, be careful of the small fan hidden away under there.