The apostrophe has two functions we all remember from sixth-grade English class.
- An apostrophe indicates the possessive case (Jessica’s bagel).
- In contractions, an apostrophe takes the place of letters or numbers that have been removed (is not becomes isn’t, Patent No. 5,269,211 becomes ’211).
Apostrophes always point downward. If the smart-quote feature of your word processor is on, then type an apostrophe with the same key you use to type a straight single quote ( ' ). Your word processor will convert this character to a curly apostrophe ( ’ ). Or you can type an apostrophe directly, using the same key as a closing single quote.
Wrinkles arise when an apostrophe is used at the beginning of a word (again, assuming your smart-quote feature is on). If you type the phrase:
In the '60s, rock 'n' roll
This will be displayed as:
In the ‘60s, rock ‘n’ rollwrong
The problem here is that the characters in front of 60s and n’ aren’t apostrophes — they’re opening single quotes. They point upward. What you need is an apostrophe in place of each sequence of omitted letters, so the result looks like this:
In the ’60s, rock ’n’ rollright
To get this result, you have two choices. You can manually delete the incorrect marks and type apostrophes directly. Or you can type straight single quotes twice:
In the ''60s, rock ''n' roll
These will be displayed as:
In the ‘’60s, rock ‘’n’ roll
Then you can delete the unneeded opening single quotes, getting you back to:
In the ’60s, rock ’n’ rollright

Very surprised at this advice. Maybe it’s meant to be word processor-agnostic, but in Microsoft Word (the de facto standard), simply typing CTRL-(apostrophe)-(apostrophe) gives you a proper apostrophe rather than an opening single quotation mark.
The typographic advice here applies to any word processor. Additionally, the book includes specific shortcuts for Word, WordPerfect, and Pages. Your tip appears on p.57.
This is the first example I’ve seen on the website where the recommendation is visually less appealing than the mistake. Is the rule of an apostrophe always pointing downwards really still pertinent?
I’m an Editor in Chief for a national magazine, and I loathe that stupid rule.