Note that in American English, periods and commas always go inside quotation marks, while the placement of question marks and exclamation points depends on whether they apply to the whole sentence or to the quoted matter only.
But while these basic uses of quotation marks are pretty straightforward, two entries in the "Associated Press Stylebook" point to the source of all the confusion. The first entry to note is the entry titled "unfamiliar terms." It reads, "A word or words being introduced to readers may be placed in quotation marks on first reference": The tuft of hair on the back of a horse's ankle is known as a "fetlock."
This explains why a restaurateur might see fit to put quotation marks around "egg foo yong" or even "special." But here's where this gets ironic: AP also explains that quotation marks can be used to designate irony. Try our "scrumptious" egg foo yong, therefore, could be using quotation marks to identify a word used by a restaurant critic or to introduce a word the sign maker doubts customers know. But most likely, the quotation marks around "scrumptious" will be read in that last sense — ironically — suggesting you'd be better off eating at the poodle groomer's.