Other DIY Testers
Active vs Passive Testers
An "active" tester is one that generally has its own battery or other power source, and it provides some kind of electrical pulse or current to the circuit being tested. "Active" testers are generally used when a device is not powered on. Care must be taken in selecting what parts of a circuit are being tested so that power from the tester itself doesn't damage any sensitive electronic components on the device being tested. Active testers are therefore widely useful for testing physical electrical devices and not necessarily sensitive electronic devices such as IC chips. A simple way to think of an active tester is one that PUSHES electricity into the device being tested.
A "passive" tester is one that generally gets its power or signal from the device being tested, which means the device being tested must be powered on. As such, great care must be taken so that short circuits aren't created, which could not only be dangerous to the user, but damaging to both the device and the tester. An example of a passive tester might be an oscilloscope or volt meter (DVM/VOM). A simple way to think of a passive tester is one that PULLS electricity from the device being tested.
Simple circuit continuity tester
You can build a simple circuit continuity tester with just a few parts. This is an active-type tester and would allow testing a cut or broken extension cord to discover which wire connects to the wide terminal (common) and which wire is the narrow terminal (hot) at the plug end. (Of course, disconnect the extension cord from the wall socket first!). You could also use it to test the ends of a communication cable to discover which wire connects to which pin. If there's "continuity" (i.e. "a connection") then the LED would light. If not, the LED would remain dark. A continuity tester can also be used to check various electrical hardware components such as switches, physical connectors, plugs and jacks, etc. However, you can't use a continuity tester on everything. For example, don't use it to check a PIC chip, transistor, diode or other sensitive electronic part because they can be damaged by the tester's voltage.