Originally Posted by: GraehmeFloydI find the simplest way to learn the order is to use the sayings

Ha! I was gonna say something similar, but Graehme beat me to it. Mnemonic devices work extremely well when trying to retain information such as this. At the risk of embarrassing myself, I will share the ones I used way back when (and still remember) with the order of sharps and flats:

Sharps (FCGDAEB): Fat Charlie, Go Down And Eat Breakfast
Flats (BEADGCF): Boys Eat Apple Dumplings Good Charlie Fat (doesn't make as much sense, but it worked nonetheless)

And as a bonus:
Modes of the Major Scale: I Don't Pull Long Monkey Arms London

I guess the more ridiculous, the better it worked for me. Cheers!