As most of the others have said, it's very likely to be a wiring problem and not a solenoid or starter problem. You need to check this first.
A multimeter is of some value in checking, but it won't tell you everything. This is because the meter needs only a tiny current
to measure voltage, while the solenoid and -- especially -- the starter require a lot more current
It is possible to measure current drop in several places and ways, but as you said you're not really familiar with the use of the meter I'd approach the problem in a very simple, brute force way.
Be sure the battery
switch is OFF. Then:
Check every bit of wiring, both to the solenoid and to the starter. Common problem: a bad ground. Check the big ground wire going to the engine
. Take it off carefully, clean it, and reattach it. Ditto for the big red wire going to the solenoid (that provides the juice for the starter). Be sure the smaller wires going to the solenoid are making good connection, both with the posts on the solenoid and within the ring terminals themselves. Are they clean and tight? Replace any suspicious terminal.
Check the ignition switch terminals as well. If there's a connector block in the wiring harness somewhere, open it, squirt some de-ox in, and reassemble a few times to get thru the surface corrosion.
Check the battery cables
where they attach to the battery, and to the battery switch. You're looking to find clean, tight connections.
Now, use your multimeter to check battery voltage. It should be 12.6V minimum with the batteries resting. Turn on the battery switch. Test the voltage at the large solenoid post (red wire). It should be the same as at the batteries. While you're measuring that, have someone turn on the starter for just a few seconds. If the voltage falls below 10.5V, either your battery is bad or the wiring is too small or there's still a bad connection somewhere or the starter itself is bad.
There are some excellent troubleshooting scenarios in Nigel Calder's books
, and in Charlie Wing's book. They would make good reading this winter :-)
Let us know how it turns out, OK?