Questions regarding battery, charging and starting problems are frequently asked here, expecially this time of year, and diagnosis is straightforward provided the correct approach is taken, so I thought a guide was in order for future reference:
From a practical point of view it is useful to know that the battery terminal voltage under various conditions can tell us almost everything we need to know about the state of the battery and charging system so accurately measuring the terminal voltage is key to fault finding in this area.
A cheap digital multimeter the like of which is available in Maplins or at most motor factors is the perfect tool for the job. Set it to a voltage range of around 20 volts DC if it has manual ranging, ensure that the test leads are inserted in the connectors marked "common" and "V" and connect them across the battery terminals, ideally with crocodile clips so you don't have to hold them conencted while you perform the tests. DO NOT connect a multimeter on the Amps range across a car battery, and make sure the test leads are not left in the "common" and "A" connectors.
Battery condition and charging circuit
Obviously the circumstances in which you find yourself with a starting or charging problem can vary, but in an ideal situation, when faced with a problem, I like to take the following sequence of actions to diagnose the fault:
1) Try to charge the battery, ideally using a mains powered battery charger for a couple of hours, to ensure it is likely to be fully charged.
2) Allow the battery to settle for perhaps 15 minutes after charging so the terminal voltage reflects its' true condition.
3) Measure the terminal voltage of the battery.
4) Apply some load (e.g. car headlights) and watch the terminal voltage for a minute or two.
5) Switch off all loads, start the engine, and, ideally, have someone watching the battery voltage while cranking the engine.
6) Measure the terminal voltage with engine at a normal idling speed.
7) Increase engine speed to a fast idle (2,000 RPM) and measure the voltage.

Add some electrical load (headlights, blower fan, heated rear window) and measure the voltage at idle speed.
9) Increase engine speed to a fast idle (2,000 RPM) and measure the voltage.
10) Check electrical connections to battery, starter and alternator and also all chassis ground connections in the engine bay for heat.
I interpret the readings taken above as follows:
3) Normal reading would be 12.5 - 12.8 volts indicating a healthy battery fully charged. Suspect battery if it has failed to reach and stabilise at this voltage after a charge.
4) Expect the voltage to drop to perhaps 12.2 - 12.5 volts due to internal resistance but to remain stable for a minute or two. If voltage continues to gradually decline below this level, and certainly if it reduces to 12.0 volts or below within a minute or two, and was previously fully charged, suspect battery.
5) While cranking, battery voltage will fall significantly. If it falls below 10 volts or so when battery was previously fully charged, I'd suspect the battery. If it's also cranking the engine rather slower than usual, it adds more weight to this diagnosis.
6) Expect 13.5 - 14.5 volts. Greater than 14.5 volts indicates battery is being overcharged (voltage regulator failed within alternator). If it's significantly greater than 15 volts do not drive the car until resolved as the battery could be damaged or even explode and other electrical accessories in the car may be destroyed.
7) If the voltage didn't make it to at least 14 volts when idling it should do now otherwise alternator suspect, or perhaps wiring from alternator to battery or chassis and engine block to battery negative terminal connections. Should remain under 14.5 volts, as before.

Expect perhaps 13.0 - 14.5 volts. voltage may well have dropped due to load on the alternator.
9) Expect 13.5 - 14.5 volts. Most of the drop with load in the previous step should recover at normal cruising RPM. If not, suspect alternator or wiring fault.
10) Electrical conductors may become slightly warm to touch with electrical load, but any conductors, or particularly crimped connections, that become hot to the touch have a high resistance (loose crimp perhaps?) and are reducing the effectiveness of the charging system. It doesn't take much voltage drop before the battery is not being adequately charged so rectify poor connections before they leave you stranded.
It may not be practical to perform the whole sequence above if you are stranded in a rainy layby. However, the battery terminal voltage will still give you some vital clues as to what's going on:
Engine stopped
No load: < 12.5 volts : Battery not fully charged or defective
Dropping to < 12 volts under load : Battery flat or, most likely, defective
Engine Running:
< 13.8 volts: Battery not being charged adequately. Ideally expect to see 14.0-14.5 volts at cruising RPM with normal levels of electrical load