While some commas are a matter of style, most are there because they have to be. Here are the main rules.

A series of items in the text

To prevent ambiguity in lists, use the serial comma—the comma immediately after the “and.”

Tax credits have been extended for wind, solar, and geothermal systems.

Not every sentence needs the serial comma in order to avoid ambiguity, but enough sentences do, including long, involved sentences whose component parts easily slide into one another, that a consistent practice must use the serial comma.

Between major parts of a sentence

Two complete sentences joined by “and” (where both halves include a subject and a verb) are separated by a comma.
•    The PUC is scheduled to hear the rate case in January, and utilities are prepared for an uphill battle.

When only the verb is repeated, this is a single sentence and no comma follows the “and” (unless (and this is a question of style) they are very long and a comma would aid in comprehension.
•    The PUC is scheduled to hear the rate case in January and will provide specific dates in December.

To set off a section of text within a sentence
Commas can set apart a section of text. Whenever a comma is used to begin setting off the text, a second comma is needed at the end of this text. (That second comma is often forgotten.)
•    My neighbor, a teenager with her sights set on engineering, often asks me about my photovoltaic system.
•    She was born in Minneapolis, MN, and attended high school in Connecticut.
•    The conference was held on September 21, 2012, at the public library.