Today's question from an author is a common mistake and misnomer. If you want the new rules of style in terms of word processing and digital printing, invest in the book The Mac is Not a Typewriter.
Today's question: do you still put the double space after the period?
Old rules of business writing and even academic writing suggested we use the double space. Today the computer does it for us, and there is no need. Word processors put the right spacing in for the user. Older writers unfamiliar with the change in the rules still add the double space, which is unnecessary and removed during editing. The double space was used in typesetting methods where typesetters physically put the "plates" together with the words and used the spacing to distinguish between the end of the sentence and the start of the new one. Since the computer can now automatically do it, and the new digital printing methods don't require plates, it's gone away.
Underlining titles now works the same way. The underlining used to be applied because we could not italicize words with a typewriter. Since we can italicize, underlining is no longer used. In fact, underlining is distracting and messing looking. Specific style rules apply to italicizing vs. quotation marks. For example, names of songs use quotation marks. Names of albums or whole works use italicize. The New York Times features an article on "Proper Grammar" by Michelle Gamble.
There you have it! Today's style lessons.