In cars with carburetors the air cleaner is a part which resembles a shallow pot resting on top of the carburetor (usually). In order to remove the lid of this pot, you must usually unscrew a wing nut. Upon removing the lid, you will hopefully discover a pleated ring of paper that looks a bit like a coffee filter without a bottom. The pot is the air cleaner housing, and the paper ring is the air filter.
In fuel injected cars, the air cleaner will probably be found at the end of the air intake hose. The cover might be held on with spring clips. Use a screwdriver to slide them off. The filter may be rectangular. In any case, if you know the make, model, and year of your vehicle, you should be able to find the right one at any auto parts store.
If you wish to replace the filter (you probably do), simply lift the old paper ring out, and put a new one in. Do not drive around without one, as your engine will become full of gunk, and grime, and it will die, and you may cry. By replacing your dirty old air filter, you may improve air flow to the carburetor, which may result in better perfomance and/or fuel economy.
Sources:
- AAA : Your Car : Air Filter - http://www.csaa.com/global/articledetail/0,8055,1004010303%257C2033,00.html
- Checking Your Air Filter - http://www.dummies.com/lifestyle/home_and_garden/auto_repair/0-7645-5089-6_0002.html