Here's a checklist:
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.
See
http://www.fluke.com/application_notes/automotive/circuit.asp?AGID=1&SID=103#volt for a diagram on how to do voltage drop testing
1.) Will the car start if it is jumped? Then clean battery terminals and check the battery. Most auto parts stores will do a free battery check if you bring them the battery.
2.) Check the battery to engine block ground, and the ground behind the engine to the firewall.
3.) Check the cables for cracks in the insulation, and corrosion around the wire where it joins the connector. Look for swelling of the cable’s diameter which would indicate corrosion inside the cable. Bending the cable can often reveal corrosive damage inside the cable when the outside looks OK.
4.) Put the car's transmission in neutral or have someone press in on the clutch. 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.
5.) .) 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. See
http://www.autozone.com/images/cds/gif/large/0900823d80195960.gif for a very good diagram of the starter & neutral safety switch wiring
6.) 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 are good. The starter relay is also known as a starter solenoid. If jumpering the two big solenoid posts made the starter crank, the logical next step is to replace the starter solenoid (also known as the starter relay).
7.) 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.
8.) Pull the starter and take it to Autozone or Pep Boys and have them test it. If the starter fails the test, then replace it. If you got this far, the starter is probably bad.
Rear mounted battery wiring.
One 1 or 1/0 gauge (or larger) from battery positive post to the battery side of the front mounted starter solenoid (relay). You may wish to place a battery shut off switch in the wiring between the battery and the starter solenoid. Be sure to remove the old battery cable that was connected to the battery. Do not remove or move any other wires. That includes any wiring for the alternator.
Follow this plan and you will have zero ground problems.
One 1 gauge or 1/0 gauge wire from battery negative post to a clean shiny spot on the chassis near the battery. Use a 5/16” bolt and bolt it down to make the rear ground. Use a 1 gauge or 1/0 gauge wire from the rear ground bolt to a clean shiny spot on the block.
One 4 gauge wire from the block where you connected the battery ground wire to the chassis ground where the battery was mounted up front. Use a 5/16” bolt and bolt down the 4 gauge engine to chassis ground, make sure that it the metal around the bolt is clean & shiny. This is the alternator power ground.
Crimp or even better, solder the lugs on the all the wire. The local auto stereo shop will have them if the auto parts store doesn't. Use some heat shrink tubing to cover the lugs and make things look nice.
The computer has a dedicated power ground wire with a cylindrical quick connect (about 2 ½”long by 1” diameter. It comes out of the wiring harness near the ignition coil & starter solenoid (or relay). Be sure to bolt it to the chassis ground in the same place as you bolted the alternator power ground. This is an absolute don’t overlook it item for EFI cars