Better yet, put a voltmeter across the terminals of the battery--not the terminal wires, the posts themselves. Have a friend try to crank the engine for two or three seconds.
If the voltage drops below 10v, replace the battery. If the voltage is above 10v, start moving the positive meter probe up the wiring to the starter, and test on each side of every junction and switch. Wherever you find that the voltage drops more than 0.4 volts across a junction, wire, or switch, you need to clean or replace it. If you don't find the voltage drop on the positive side, look on the ground side.
Another clue is that the problem area will get warm.