Some autoparts stores will test your battery for you (for free).
I don't know the exact voltages but here is what I have done when I suspected my battery/charging system:
1) Start the car and get it to fast idle. Measure the voltage at the battery. Up to about 14 volts is okay I think. If it is much higher your regulator may be bad and overcharging (and killing the battery).
2) With the engine still running, turn on the head lights, fan, rear window defogger etc. Measure the battery voltage again. If it is below 13V then you may have a charging system problem that eventually runs your battery dead (in city driving).
3) Turn off engine but leave headlights etc on. The voltage will drop to 12-point-something. If it keeps dropping and goes below 12V then you may have a bad cell in your battery.
Maybe someone can give more detailed voltages rather than my ballpark ones.
[Edit: here's a link with some numbers:
http://www.2carpros.com/how_to/battery.htm ]
Greg
all fine tests in the first reply.
[disclaimer: the following suggestions come from an unlicensed "shade-tree" mechanic who has been working on a cars for 40+ years. if a REAL automobile technician chimes in here and contradicts anything below, do what i would do - take the REAL technician's advise. please note also, that as i've gotten older, i don't work on as many cars as when i was younger, so by today's standards of the last 10yrs or so, my experience if more limited and may not always be applicable.]
here's more that you should do.
try to conduct the following tests at around 70degF if at all possible as lower temps can affect the results. however, if you live in very cold climes, it might be more important to conduct the tests at lower temps, but that can affect the results.
0) i'm going to skip what may be an important test method which a Pro would do as it involves applying draining off surface charge and then applying very specific loads to the battery. We'll leave that to the Pro, not that it's that difficult to do, i've found with my limited experience that the below tests are sufficient.
1) starting draws the most current. you will need a voltmeter to perform this test. since designs are different nowadays, do what you need to do to prevent the engine from starting when you crank the starter (this could be as simple as disconnecting the coil wire or more complicated for some coil on plug designs).
measure the battery voltage while cranking the starter. shouldn't fall below ~11.5V for a strong battery. around 10.5V you should check the electrolyte level and specific gravity (if you are able to) and recharge the battery. if it falls to ~9.5-9.7 V - replace the battery is my suggestion. i've found that they won't hold a charge when the cranking voltage gets that low (they also won't start - older american muscle at least, as they're turning over too slowly).
2) you will need an inexpensive BATTERY hydrometer (NOT the same as an anit-freeze/coolant hydrometer) to perform this test. if you are able to pop the caps off of the battery, measure the specific gravity. since the acid is mixed with water you [EDIT] WON'T [/EDIT] get a 1.42 specific gravity (the specific gravity of 16Normal sulfuric acid, if i recall correctly). anything above 1.24 should be 'ok', IMO.
3) last but not least (and it should really be the FIRST test that you do) is to inspect all of the battery connections for corrosion and to insure that they are tight. inspect the engines individual belts or serpentine belt while you're at it. also, inspect the underside of the hood for traces of fluid thrown up onto it by the rotating belt(s) when the engine is running. this can often be one of the first signs that you have a fluid leak. if you find traces of fluid on the underside of the hood, look around for the closest source(s) of fluid or areas nearest the belt(s) where fluid could have leaked and gotten onto the belt(s) and thus be flung onto the underside of the hood - not battery related, but a good thing to look for. Also, make note of your fluid reservoirs. Low fluid can mean a leak. In the case of the brakes, it could also mean that your brake pads are worn or very worn, so if you can't find any leaks in the braking system, don't just refill the reservoir, check the thickness of your brake pads (or have a Pro do it).
we did NOT cover testing the automotive charging system here. the first reply did address that a bit.
[Note: as i have "old-timers" and often have trouble recalling certain info, please double check my "numbers" with a more reliable, current, up to date source.]