A relatively inexpensive yet useful item to have on hand is a battery hydrometer, available at any auto parts store. A battery with a weak cell, will still read 6 (or 12) volts between the two terminals, but as stated above, may not have enough cranking capacity to engage the starter. Thus, sometimes just measuring battery voltage may not tell you much about the battery.
Presuming the battery is not of the sealed type (that is, you still have access to each cell), then taking a specific gravity reading on each cell with the hydrometer will frequently point up the weak cell (similar to a compression check). Typically, a fully charged lead-acid battery will have a specific gravity around 1.280 (sometimes spoken “1280”) so that if you get a series of readings for the cells of around 1.265 to 1.280 but one cell reads 1.090 (for example) you can presume – if this cell doesn’t return to normal with charging – that this cell has failed and the battery ought to be replaced.
If, on the other hand, the electrolyte level covers the plates, all specific gravity readings are fairly consistent (+/-) and increase with charge (and come up to somewhere around 1.280) then the battery is probably good and the problem lies elsewhere (elsewhere being – usually – corroded terminals/connections or a failed component, depending on the problem).
If all the battery cell specific gravities are consistent but do not increase (significantly) with charging (or the charging rate in amperes doesn’t decrease with time) the battery has reached the end of its life and should be replaced.
If the battery is a fully-sealed unit, and you don’t have access to the cells, then the only reliable test I know of to ascertain battery condition is a load test that actually puts a resistive load on the battery long enough to determine if it’s still good.
When you are done measuring the specific gravity, rinse the hydrometer out with tap water so that the electrolyte (sulfuric acid, H2SO4) doesn’t get all over everything.
And if you need to top off the electrolyte level, use distilled water (please don’t take offense at this advice, inasmuch as you never know the experience level of whomever posts the original question or reads the subsequent replies). Small amounts of tap water will not cause the battery to instantaneously go belly-up, but the minerals in most tap water (and the chlorine – or whatever treatment agent your municipality uses - in many municipal water supplies) don’t help battery life.
Btw, if you don’t have a battery hydrometer but do have a multimeter, you can actually read the voltage from one terminal through each cell successively by momentarily dipping one multimeter probe tip into the electrolyte. Thus, starting with the grounded terminal of the battery, you should see about 2 volts between that terminal and the first cell, 4 volts between the ground terminal and the second cell, and so on (each lead-acid cell generating about 2.2 volts DC which – with internal resistance – results in about 2 volts per cell). Rinse off the electrode tip when done.
And, lastly (based on my experience on several occasions following my forgetting to turn off the lights after parking my coupe) you would be surprised how many times you can start your Model A with the hand crank and a supposedly “dead” battery. If you know how to do this (there is a good description and photo under “hand cranking” in the Victor W. Page’ “Model A Ford Construction, Operation [and] Repair for the Restorer”) this may help tell you whether you have a battery problem or starter (or ignition) problem without schlepping the battery back to the auto parts store. Besides, imho, every Model A driver ought to know how to start his/her Model A with a hand crank.
Ok, a long post and probably more than most want to know about lead-acid batteries. At least I didn’t include the battery equations (once a submariner, always a submariner…)