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.
In a negative (-) earth-return system, the current flows from the positive (+) terminal to the component being operated. The component is earthed to the car body, which is earthed to the negative (-) terminal of the battery.
The two components are connected in series so that the varying resistance in the sender will affect the position of the needle on the gauge.
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.