A common problem with older homes is blown fuses. Fuses work just like circuit breakers do in newer homes - they protect fixtures and wiring by turning off the power if the circuit becomes overloaded. There are two types of fuses - cartridge fuses and screw-in fuses. First, you'll need to identify which type of fuse is required, and then select a replacement fuse with the EXACT SAME amperage rating. Most ratings are listed on the side of the fuse with 15 and 20 amps being the most common types.
You should also take a moment to look at the fuse being replaced. If the window on the fuse is blackened, that means the fuse short circuited. But if the fuse has a clear window, that means the circuit was overloaded. Overloaded circuits could cause electrical fires, but can be easily be corrected by moving a fixture to a plug wired into a different circuit.