To easily remember the order and names of all the sharps and flats in the scales, simply memorize the following two phrases.

For sharps

Fat Cats Go Dancing And Elephants Boogie
(F# C# G# D# A# E# B#)

 

For flats

Boring Ed Always Drove Good Clean Fords
(Bb Eb Ab Db Gb Cb Fb)

 

These two sentences should help you through your whole career as a musician 😉.

Fun fact: You will also notice, that you can just read the sharp mnemonic from the end and get the flats and vice versa. The reason for this is the circle of fifth! Going right in the circle of fifth means using sharps, going left means using flats – and after half a circle (at 6 o’clock so to speak) they meet 😄.