I am going to use sentences from T.S. Elliot’s Old Possum’s Book of Practical Cats for examples. Since he sometimes used poetic license with his punctuation, I may sometimes use prose license and make some small changes.
Parenthetical Clause: “Parenthetical clause” is a big phrase for something in your sentence that can be removed without changing its basic meaning. Usually the extra words are there to add some flavor. Use one comma in place of an opening parenthesis and another comma in place of a closing parenthesis.
If the parenthesis would be at the very beginning or very end of the sentence, do not put the comma at the beginning or the end.
Comma before and after the clause
The reason, I tell you, is always the same.
Comma after the introductory clause
As she finds that the mice will not ever keep quiet, she is sure it is due to irregular diet;
Comma before the closing clause
Her coat is of a tabby kind, with tiger stripes and leopard spots.
Joining two sentences with a conjunction: A conjunction is a connecting word, such as and, but, or so. If you have a comma after the conjunction, both sentences must be complete sentences. A complete sentence must have a subject and verb.
He likes to lie in the bureau drawer, but he makes such a fuss if he can’t get out.
They like to practice their airs and graces and wait for the Jellicle Moon to rise.
Series: A series of words separated by commas, conjunctions, or both.
He has lunched at the Tomb on cabbage, rice pudding, and mutton.
Jellicle Cats are black and white.
References: I found a terrific, succinct online 150-page book about Business English: The Essential Handbook for Business Writing. Download this to your computer and review it. (You may also want to add to your personal library Old Possum’s Book of Practical Cats by T.S. Eliott, too.)