Apparently there are questions about charging batteries.Here is the link to the charger that was provided with each kit from Sparkfun.
Here is the link to the batteries that were provided with each kit from Adafruit.
There is an LED on the battery charger that indicates that the charging cycle is finished. The LED will be on when charging and off when complete. A description is provided on the Sparkfun website along with schematics if you are interested. Here is the datasheet for the chip they are using that provides even more detail as to how it works.
It seems that sometimes the charger will not go into the charging mode when the battery is first plugged in for whatever reason. You may have to cycle the battery in and out of the connector to get the charging mode to start. A fully charged battery will measure 4.2 volts as measured with a volt meter with the battery disconnected from anything.
Make sure your batteries are fully charged and tested for Eclipse Day!