Originating in the U.S. Army of WWII, this is the shorthand slogan to describe the hygiene preparation an enlisted soldier must do to ready himself for a military inspection by superiors.
"Shine" refers to the careful and thorough polishing of one's black military boots.
Now it has entered civilian use to mean preparation for any important social event in which one must look good, often abbreviated nowadays to just "shit, shave and shower".
Soldier 1: "We've got an inspection later today from the brass."
Soldier 2: "Guess it's time to shit, shave, shower and shine."
Fogey/fogy /fougi/ sl. (early 18C+, orig. Scot) old-fashioned, stuck-in-the mud.
Person with old fashioned ideas which he is unwilling to change: Come to the disco and stop being such an old fogey!
You think me an old fogeyand an old tory, his thoughtful voice said. I saw three generations since O’Connel’s time. I remember the famine. Do you know that the orange lodges agitated for repeal of the union twenty years before O’Connel did or before the prelates of your communion denounced him as a demagogue? You fenians forget some things. (James Joyce, Ulysses. Penguin Books,1992. p. 38)