Semicolon use is really tricky. To be honest, I f–k it up quite a lot, so I guess my writing is full of errors. I wrote a 90 page thesis in order to graduate from university, and I probably didn’t use a single semicolon in it. There are a few things you should remember, though.
If you have two independent clauses with a coordinating conjunction between them use a comma before the coordinating conjunction. Like:
“I will go to the restaurant tomorrow, and I plan to order a hamburger.”
If you have two independent clauses and there is nothing between them, use a semicolon. Like:
“I will go to the restaurant tomorrow; I plan to order a hamburger.”
If there are two independent clauses and you have a conjunctive adverb between them (the sorts of things we usually refer to “transitional phrases” in this group like moreover, therefore, consequently, thus…) use a semicolon before the conjunctive adverb, and a comma after the conjunctive adverb. Like:
“I will go to the restaurant tomorrow; moreover, I plan to order a hamburger.”
“It is raining today; therefore, I will go to the restaurant tomorrow.”
Part of the problem is that a lot of native speakers (myself included) often forget about the semicolon in the last example and just use a comma after the first clause. As in:
“It is raining today, therefore I will go to the restaurant tomorrow.”
This usage is so common that I’d pretty much call it “correct.”