We all know what a semicolon looks like. It's the dot and comma. Like this - ;
How do we know when to use them? First of all, it connects independent clauses. You know, those complete sentences.
"Suzy loves cats; she loves them so much, she made a kitty shrine in her bathroom."
You could easily write this sentence as two sentences. But with a semicolon, you are connecting them in a different way. You are showing the close relationship between these sentences.
You also need a semicolon if there's a conjunction in front of it: therefore, nevertheless, besides, etc.
"My mother and I never cut our hair; besides, the lock of hair was black, not brown."
Note the comma after the conjunction. Also necessary. Again, you can rewrite it. This one, you could have used a comma and an "and". But the semicolon makes the sentence shorter, and as a writer you know to avoid making everything too long.
Those are the two main points of semicolons. I cannot think of other uses, but if you do, then comment. Here are some more examples:
"She read The Scarlet Letter; it was boring and long, but at least it wasn't Twilight."
"He wished on a shooting star; therefore, he thought his wish would come true."
"Mary studied five hours a night in preparation for her exam; nevertheless, she got a C."
"John played sports and was really popular; everyone loved him and looked up to him."
Anyways, there is your lesson in punctuation. Keep writing, don't steal, eat your vegetables. Have a wonderful rest of the week! :D