2003 Nissan Altima won't start?

A car needs 3 things to start. Air, fuel, and spark. Check that it can get air by removing the air cleaner and inspecting it. Leave the air cleaner off for now. Try a squirt of starting fluid into the carburetor (not a lot mind you, just a quick squirt). Be prepared to quench a flame if the engine backfires through the carburetor (have a wet towel handy). Crank the engine. If it fires, you have spark. If it does not fire, you have ignition problems. If it fires and stalls out quickly, you have fuel problems.
For fuel problems: Be sure you have gas! (I know it is obvious, but check the tank!). If the car has not been used for awhile, the gas may have gummed up the carburetor. While it is possible for the weekend mechanic to take a carburetor apart and clean it, it is probably best left to a professional mechanic. Verify that you are getting gas to the carburetor by detaching the rubber gasoline hose at the carburetor. Most cars today have electric fuel pumps, so turning on the ignition should result in a stream of fuel from the gasoline hose. If not, crank the engine and see if a mechanical fuel pump moves the gas. If you get no gas, find out why or your car will never start. If you get gas, the carb is probably gummed up. It is best to conduct this last test into a mason jar to catch the gas, and it is best to postpone the cigarette break until after the test is complete.
If you suspect the ignition, pull a spark plug. It should look clean and whitish to light coffee color. If it is filled with carbon and oil, you have other engine problems. You can look for an ignition spark by laying the plug case against the engine while it is attached to the distributor wire. Crank the engine and you should see a spark jump the gap at the spark plug tip. This spark is often small and hard to see in sunlight. Do not perform the spark plug test in the temporal vicinity of the fuel test. A hot spark with gasoline nearby is dangerous.

A car that turns over means that at least the battery is good. Try next to insure it has air, gas, and spark.