U = Top(Up) D = Down (Bottom)
R = Right L = Left
B = Back F = Front
Letters without an apostrophe mean turning clockwise, while letters with an apostrophe mean turning counterclockwise. Imagine a little watch built into the center square of each face. Clockwise moves, such as F,R,B,L,U,D should follow the clock hands, counterclockwise moves, R',F',B',L',U',D' go in the opposite directions than the clock hands. Another rule of thumb is that if you twist with your right hand, clockwise means following your thumb provided your palm is resting on the face (this is important especially for the D, D' moves when people make occassional mistakes).
The little "s" behind letters means the "slice move" when two opposite faces move into the same direction. For example,
Ls = L and R', Rs = R and L', Ds = D and U', Us = U and D', Fs = F and B', Bs = B and F'.
Ls'= L' and R, Rs'= R' and L, Ds'= D' and U, Us'= U' and D, Fs'= F' and B, Bs'= B' and F.
When the letter is followed by "a", this means the "anti-slice move" when two opposite faces move into opposite directions:
Ra = La = R and L, Da = Ua = D and U, Fa = Ba = F and B
Ra'= La'= R'and L', Da'= Ua'= D'and U', Fa'= Ba'= F'and B'.
The graphics shows the top view of the cube with the last, unsolved layer being the U side.
The numbers in brackets show the length of each lagorithm in four different countings: (face, quarter, slice, antislice)
You can easily see that the quarter move counting is always the longest, while the antislice counting is always the shortest. Denoting the number of moves in the four diffrent countings as F, Q, S, and A, we can write Q > F > S > A.