How to properly use ';'?

The semicolon ( ; ) has only one major use. It is used to join two complete sentences into a single written sentence when all of the following conditions are met:

(1) The two sentences are felt to be too closely related to be separated by a full stop (called a 'period' in US English)

(2) There is no connecting word which would require a comma, such as and or but;

(3) The special conditions requiring a colon ( : ) are absent.*

Here is a famous example:

It was the best of times; it was the worst of times.

A semicolon can always, in principle, be replaced either by a full stop (yielding two separate sentences) or by the word and (possibly preceded by a joining comma). Thus Dickens might have written:

It was the best of times. It was the worst of times. or
It was the best of times, and it was the worst of times.

* A colon is nearly always preceded by a complete sentence; what follows the colon may or may not be a complete sentence, and it may be a mere list or even a single word. A colon is not normally followed by a capital letter in British usage, though American usage often prefers to use a capital. Here is an example:

Africa is facing a terrifying problem: perpetual drought.