Commas and compound sentences
I would not even go into this, but one of my thesis students told me that he didn’t know it (after I’d spent 2 years assuming he was making a stylistic choice). Compound sentences are linked with a conjunction and a comma, or a dash, or a semi-colon. That is: if a sentence is made up of two complete clauses (sentence and verb), there should be a comma, dash, or semi-colon between them. Examples: “She was washing her clothes, and she thought she’d wash his.” Do you see how each of the clauses on either side of the comma could stand as a sentence on its own? That’s what I mean. Let’s try it another way: “She was washing her clothes–and she thought she’d wash his.” That would work, and it would be correct with a semi-colon in place of the dash. Or you could drop the “and,” in which case you should NOT use the comma, but a semi-colon or dash would work: “She was washing her clothes; she thought she’d wash his.” It’s a matter of joining two sentences/thoughts that have more of a natural link than 2 separate sentences might/would.
Appositives
Also, put commas after appositives. The girl, a crazy person, was coming. Or: We went to the house, a very nice place.
Commas, generally
Don’t put commas after “but,” except in very rare circumstances (that I can’t think of offhand). “But, it didn’t work.” No, that’s wrong. If it’s dialogue, or if you really need a pause after “but,” go ahead. But as a matter of course, this doesn’t work. I think of commas in terms of breath pauses in speech, or as moments in which something happens: She stopped talking, then sat down. The comma is the space in which she sat, you see. It’s all very logical and natural, as long as you’re not intimidated. That is, finally: grammar and punctuation work best when you know what you’re doing, when you know what things mean, but, most importantly, when you allow the sense and sound of what you’re saying to guide you.