Step 1: Description
In any case, it is essential that some points are connected together, and equally essential that some other points are NOT connected together. A continuity tester enables you to quickly check whether points intended to be connected are really so, and that points intended to be isolated are also really so. Such a check is usually performed on a circuit board before any components have been loaded into it.
The technician's instrument of choice, the multimeter, is not really suited for a quick check. It gives you a reading, which then has to be interpreted. However, some meters do have a "continuity" position with a beeper for this purpose.
I have here attempted to provide instructions to make a small intrument with visual indication of continuity, suitable for checking continuity of conductors, low value resistors and high value capacitors. It is not suitable for checking semiconductor devices. It might be possible, depending upon your LED, to check diodes with it.