At times while on the site, a popup appears with a link to the question offering the publicist badge. I've pasted the link into Facebook, etc. but I have not gotten the publicist badge. Is there a trick for this?
Yes, the trick is that 1000 people have to follow the link. The Announcer badge is easier at only 50 clicks. There's also the "Booster" badge at 400 clicks.
Other than that, you just have to make sure to use the link you get from clicking "link" on the question (or from the popup), that ends with two numbers, like "q/1168/76".