Rule #1 - this is in your notes already

Use a semicolon between two independent clauses that aren't joined by a coordinating conjunction (for, and, nor, but, or, yet, so).

Examples:
I wasn't paying attention to where I was going; I was checking my messages on my phone.

DO NOT put a semicolon if you use a conjunction.
X I was checking the messages on my phone; so, I wasn't paying attention to where I was going.

Rule #2 - this is in your notes already

Use a semicolon between two independent clauses joined by subordinating conjunctions (phrases such as for example, instead, moreover, however, in spite of, nevertheless, etc.)

Examples:
I wasn't paying attention to where I was going; instead, I was checking my messages on my phone.

TIP:
Watch your punctuation and capitalization. Capital letters only follow semicolons with proper nouns and the pronoun "I."