Ignition, fuel and compression are the three primary reasons why a car might crank, but the engine does not turn over and start the vehicle. An engine that does not crank or cranks slowly is pointing at a starter- or battery-related problem.
Ignition can be tested using a spark tester or placing a plug wire near a good ground. If there is no spark during this test, then the culprit is likely a failed ignition module, distributor pickup or crankshaft position sensor. If the test yields spark, then the next test is for fuel.
A bad fuel pump or a bad vacuum leak that is interfering with the air/fuel ratio is usually to blame in this case. Checking pressure in the fuel lines can be done with a pressure gauge. It is also important to check the fuel gauge, as plenty of no-starts are caused by an empty or nearly empty fuel tank.
If the engine is confirmed to have both fuel and spark, then this leaves compression as the culprit. Timing belts, overhead cams and blown head gaskets are all possible causes. If the engine has over 60,000 miles on it, the timing belt might be a cause. A four-cylinder engine with a blown head gasket is unlikely to start, but six- or eight-cylinder engines with a couple of dead cylinders may still stutter to life.