To answer your question (which doesn't seem to have been addressed here except to refer you elsewhere), the circle of fifths means that each scale in the circle has one more sharp (or flat) that the previous. If you are playing the "sharp" circle of fifths, each new scale is a fifth above the previous and contains one additional sharp note.
e.g. C, G (#), D(##), A(###), E(####) etc.
In playing the "flat" circle of fifths the approach is essentially the same except that ordinarily you think in terms of lowering notes a half-step so you DESCEND a fifth to the scale with an additional flat.
e.g. C, F(b), Bb (bb), Eb (bbb), Ab(bbbb) etc.
Another way to look at the circle of (flat) fifths is to ASCEND four degrees to the scale that contains one additional flatted note. It works in either direction.
e.g. C, F(b), Bb(bb) etc.
In approaching the "sharp" circle of fifths descending you go down four degrees to the scale which has one additional sharp. E.G. C, (down four degrees to) G(#), etc.
That's really all there is to it.