Comma
In a list of items, you usually put a comma after the word “and” at the end of the list like:
I like zucchini, pumpkins, and cucumbers.
However, the comma before “and” in a list is technically optional and you can instead say:
I like zucchini, pumpkins and cucumbers.
Personally I always thought that was weird and I always use a comma before the “and” at the end of a list, but you don’t have to. It is optional. Commas have a million other uses; you can check Wikipedia for those other ones.
Semicolon
A semicolon I find most people don’t know how to use; however, I am an exception. A semicolon is used between closely related independent clauses. Basically, it’s stronger than a comma, but weaker than a period. (I use semicolons a lot because I like ‘em). :)
I like zucchini and pumpkins; I don’t like other types of squash.
You could make that two sentences, but you can also use a semicolon. A semicolon is also used after an independent clause and before another conjunction like:
I like zucchini and pumpkins; however, I don’t like to grow them.
A semicolon is also used in lists where the items in the list contain commas:
I have three groups of squash: yellow cucumbers, zucchini, and green cucumbers; gourds and turban squash; and pumpkins, white squash, and buttercup squash.
I find that last usage to be a bit wordy and I don’t see it used very often. You’ll probably never use it that way unless talking about cities like “Houston, Texas; San Francisco, California; and Las Vegas, Nevada”. In that case, just think of the semicolon as a big comma.