At the top of the Circle Of Fifths Diagram, the key of C has no sharps or flats. Starting from there and going clockwise by ascending fifths, the key of G has one sharp, the key of D has 2 sharps, and so on. Going counterclockwise from the top by descending fourths, the key of F has one flat, the key of B♭ has 2 flats, and so on.
The Circle Of Fifths is used in music theory to represent the relationship between Diatonic Scales. The numbers on the Circle Of Fifths chart show how many sharps or flats the key signature for this scale has. Thus a Major Scale built on A has 3 sharps in its key signature.
Tonal music often modulates by moving between adjacent scales on the Circle Of Fifths. This is because Diatonic Scales contain seven pitch classes that are contiguous on the Circle Of Fifths. It follows that Diatonic Scales a perfect fifth apart share six of their seven notes. Furthermore, the notes not held in common differ by only a semitone. Thus modulation by a perfect fifth can be accomplished in a very musical fashion.
In order to remember which order that the sharps and flats of a key signature are written, there are several mnemonics that can help: The order of the sharps is Fat Cats Go Dancing At Eds Broiler. From this you can say that if you know the key of E major has four sharps, the mnemonic shows which sharps they are (F,C,G,D). The mnemonic for flats is 'Boogie Ends And Down Go Cats Fast'.
