In the following sentence should there be any commas? Do I have the period properly placed?

After she began the party she said "I am going home."

Thanks for any help you can provide to me.

The rules of punctuation are confusing for a number of reasons, primarily: (1) the British rules are different from the American rules; (2) the rules are set by publishers, not by history, and different publishers may choose to set different standards, and (3) the rules change much, much faster than the actual rules of grammar itself.

With regard to your sentence:
- After she began the party she said "I am going home."

the most common understanding would be that "I am going home" is a dependent clause, and therefore should be separated from "she said" by a comma. (Having said that, "she said" is ITSELF a separate clause from "After she began the party", so you'd need a comma BEFORE "she said" as well as after it). Your placement of the period would (most probably) be considered correct on both sides of the Atlantic.

Rommie

PS. I'm rapidly coming to the conclusion that this forum could do with a FAQ specifically about punctuation. The differences between British and American standards would itself be particularly enlightening.