How to tell if your battery is dead
The following is important information for the DIY rider. Quite often a seemingly impenetrable electrical problem can be traced to a battery that is no longer serviceable. This should be the first thing you look at.
Sometimes a battery just dies. Not necessarily from neglect, age, or use. It just dies. Car batteries can give some advance warning when they start to go, but tiny bike batteries are more likely to be fine one moment and dead the next. This normally comes from sulfates building up along the bottom and shorting out a couple of the lead plates. It's difficult for many people to trouble-shoot because they'll just toss a voltmeter on the battery, see that it shows 12v DC, and right away say it's fine. The truth is, if the resting voltage (after sitting, not on a charger) is below 12.2, that battery needs to be replaced. Below 12v and it's dead, for all practical purposes.
A 12 volt battery that has only 12.0 volts is a dead battery. This sounds totally wacky, but it is true.
Here are the classic symptoms of battery failure. If any of these are present, test the battery as outlined below.
To confirm the condition of your battery, you'll need a multimeter. Follow these instructions if you don't already know how to use a multimeter. Check the voltage at the battery terminals, and make sure to record the voltage down to the tenths: 12.6v vs. 12v. Check the following values:
If your battery doesn't meet these minimums, then either the battery's dying or the charging system isn't working correctly. Unless something catastrophic has happened (like a crash, vandalism, flooding, etc.) it's very likely to be the battery. This article talks about what kind of battery to get.
If the "normal rpm range" voltage reads higher than 13.8v, your voltage regulator may be failing. This will boil the battery dry from overcharging, and eventually start popping lights and causing other damage. This should be fixed as soon as possible.
Note: Batteries on older bikes, and the occasional new battery, are not of the sealed variety. They will periodically require water to be added. Make sure the electrolyte level is full, and if it isn't, top it up with distilled water. A battery with low electrolyte will mimic the symptoms of a dying battery, but can be fully revived by adding distilled water and charging. You can tell if your battery is sealed by looking for a row of six caps (or some kind of removable strip) across the top of the battery casing.
If you'd like to know more about lead-acid batteries and their care and feeding, Yuasa produces a very comprehensive technical manual (PDF) that explains all this in detail. Yuasa batteries have a deserved reputation for excellence, which is usually reflected in their price.