A comma usually precedes a coordinating conjunction (and, but, for, nor, or, so, or yet) that joins two independent clauses in a compound sentence.

With very short clauses, writers sometimes omit the comma before and or or. You will never be wrong to include it, however.

She saw her chance and she took it.

She saw her chance, and she took it.

Always use the comma if there is any chance of misreading the sentence without it.

You may want to use a semicolon rather than a comma when the clauses are long and complex or contain their own commas.

When these early migrations took place, the ice was still confined to the lands in the far north; but eight hundred thousand years ago, when man was already established in the temperate latitudes, the ice moved southward until it covered large parts of Europe and Asia.

—ROBERT JASTROW, Until the Sun Dies

Be careful not to use only a comma between independent clauses in formal writing. Doing so creates a comma splice. Either use a coordinating conjunction after the comma, or use a semicolon.