When an electrical component stops working the fault may be in the component, in the electrical circuit or in the fuse that protects them. Because the fuse is a likely cause, and the easiest to check, look at it first.
The sudden surge of high current in a short circuit makes the fuse wire melt, or blow, breaking the circuit. When this happens, see if there is a short circuit or a disconnection, then install a new fuse of the correct amperage rating (See Checking and replacing fuses).
Some components must be connected in series. For example, the sender in the fuel tank varies its resistance according to the amount of fuel in the tank, and sends a small electrical current to the fuel gauge.
Some ancillary components can be operated without the ignition turned on by turning the switch to the auxiliary position. A radio is usually wired through this switch, so that it can be played with the engine off.