OK, I dug out my old automotive electrical textbooks to get the straight story and refresh my memory. The best information will come from specific gravity (SG) measurements with a hydrometer. This obviously requires that you can access the cells through caps on the battery. If it's one of those maintenance free batteries that are sealed, you're out of luck. If you're in a cold climate, the SG should be about 1.280 in each cell for a 100% charged battery, 75% charged should have SG of 1.230, 50% charged should have SG of 1.180, 25% charged should have SG of 1.130, discharged should have SG of 1.080.
An SG difference of 0.025 or more between individual cell readings indicates that the battery is starting to fail due to internal shorts, normal deterioration from age and use, loss of acid, etc. If the highest cell SG is below 1.190, charge the battery and retest.
You can do some tests with a voltmeter, but not across the terminals. The battery will develop a surface charge that will read on a voltmeter, but doesn't tell the real voltage of the battery. I've seen readings up to about 16 volts, but 14 is about normal. Back when I was doing this for a living, if a customers battery was in the neigborhood of 12 volts, we considered the battery pretty much dead and knew there was a problem somewhere. Anyhow, voltage measurements across the the terminals might tell you something, but they may also be very misleading. If you're making judgements based on these measurements, you might be going down the wrong road. However, if you can open your cells, measure voltage between the cells (in the electrolyte) and the battery case (don't forget to clean the probes afterward). This is called an open circuit voltage test. If the cell voltages are below 2.06 volts per cell, recharge the battery. If individual cells vary by more than 0.5 volts, the battery needs to be load tested. The open circuit test correlates directly with the SG test, and therefore may not be of great use if you've got good SG measurements.
A load test (also called a capacity test) is by far the best way to test a battery. The problems people have with them usually come from not doing it correctly. To do a load test, the SG of the battery must be over 1.220. If it is less, the battery should be trickle charged (NOT fast charged) until the battery is fully charged. Then apply a carbon pile load tester for 15 seconds and measure battery voltage. Voltage of 9.5 V or more indicates ample capacity, and if the SG was over 1.220 before testing no additional service is required. However, if the SG was below 1.220 before load testing, and the battery WAS charged, you've either got a problem with the charger or the battery is probably toast.
There are a couple more tests that you can follow past this point, but I figure that if we can't get the SG up to specs, it won't take a charge, and fails a load test, we're wasting time. The battery is gonzo.