Semicolons must go between two independent clauses, i.e. clauses with a subject and verb at a minimum, and which could stand alone as two separate sentences. Why does the semicolon exist? To link two separate sentences that are very related in meaning.
Yuna and her dog are inseparable; her dog even goes to work with her every day.
Larry is having a bad week; his house burned down and his dog ran away.
Colons introduce examples, and must follow a complete, independent clause. You should be able to substitute the words "namely" or "such as" for the colon and have a sentence that makes sense.
I have several favorite flavors of ice cream: cookie dough, bubble gum, and mint chocolate chip.
For the past several years, management has been working to solve the company's problems: high costs, poor distribution, and unreliable machinery.
Commas are used for:
(1) Lists
Beeswax is an ingredient in lip balms, soaps, and candles.
(2) To set off modifiers, particularly inessential modifiers.
The bee, which was buzzing around the flowers, was soon joined by several others.
The horse, an Appaloosa, pranced around the barnyard.
Commas should NOT be used anyplace where a semicolon would work. When you put a comma between two independent clauses, you create a run-on sentence!