Q. Apparently Americans enclose periods commas inside quotation marks, but do the British do it that way too???

A. In what is sometimes called the British style (see paragraph 6.9), only those punctuation points that appeared in the original material should be included within the quotation marks; all others follow the closing quotation marks. This system works best with single quotation marks. (The British tend to use double quotation marks only for quotations within quotations.)