Here's a checklist:
Courtesy of Stangnet's Jrichker

Check battery, terminal connections, ground, starter relay switch (also known as solenoid) and starter in that order.

A voltmeter is handy if you are familiar with how to use it to find bad connections. Measure the voltage drop across a connection: more than .5 volts across a connection indicates a problem.

1.) Will the car start if it is jumped? Then clean battery terminals and check battery.

2.) Check the battery to engine block ground, and the ground behind the engine to the firewall.

3.) Then pull the small push on connector (red wire) off the starter relay (Looks like it is stuck on a screw) and jump it to the terminal that is connected to the battery. If it starts, the relay is good and your problem is in the rest of the circuit.

4.) Remember to check the ignition switch, neutral safety switch on auto trans and the clutch safety switch on manual trans cars. If they are good, then the relay is bad.

5.) Jump the big terminals on the starter relay next to the battery with a screwdriver - watch out for the sparks! If the engine cranks, the starter and power wiring is good. The starter relay is also known as a starter solenoid.

6.) The starter may be hung, loosen up the bolts that hold it on, and give it a good whack with a big hammer. Tighten up the bolts and try again.

7.) If that doesn't work, use a jumper cable from the positive lead on the battery direct to the starter post where the big wire from the relay connects. If it cranks then, it is the power wire from the relay gone bad. This will be hard to do, since there isn't much room to do it.

8.) Pull the starter and take it to Autozone or Pep Boys and have them test it. Starter fails test, then replace it. If you got this far, the starter is probably bad.