Possibly learning how to use cos and sin to move around the bounds of the unit circle would be a good start. http://en.wikipedia.org/wiki/Unit_circle
If you are standing in the middle of the unit circle looking directly right (x = 1, y = 0) and say you want to rotate 45 degrees you would get those coordinates like this
x = cos(45.0); y = sin(45.0);
This will give you the new direction at 45 degrees from the original direction. Think about it, cos(90) gives a value of 0. This is correct because if we rotated 90 degrees, the x component of the vector (direction) would be 0, because it would be pointing directly up (x = 0, y = 1).
Hope this helps a bit, rotations are very tricky to start off learning.