The individual fuses in the box are usually numbered, so that sorting out which one may have blown is simplified by referring to the numbered list in the handbook. This should tell you which fuse protects which circuit. Where they are not numbered, take out each fuse in turn and see which component stops working.
If the battery voltage drops, less current flows, and eventually there is not enough to make the components work. The extent to which a wire resists the flow of current is called resistance, and is measured in ohms.
Current flows along a single cable from the battery to the component being powered, and back to the battery through the car metal body. The body is connected to the earth terminal of the battery by a thick cable.
The strength of the current is measured in amperes (amps); the pressure that drives it round the circuit is called voltage (volts). Modern cars have a 12 volt battery. Its capacity is measured in amp/hours. A 56 amp/hour battery should be able to deliver a current of 1 amp for 56 hours, or 2 amps for 28 hours.