I learned this method too. It's the same one written on the booklet that came with my first cube. I think this is still the traditional/simplest method. When doing the final side (3rd layer), you first get the "cross" (center pieces in the correct orientation, not location). Then you go about rotating those centers, if I'm guessing right, the part you're stuck on. I flip my cube "up side down" so the third layer is on the top. These are the moves to switch the front center and right center pieces: U, R, U, Ri, U, R, U, U, Ri.... U signifies moving the "Upper" Face clockwise (when looking at it), R, is the "Right" Face, and Ri is the right face, but counter clockwise. All these are 90 degree turns. Not sure if this helps, and you'll still need to rotate the corners for position and then for orientation after this.
If this somewhat seems familiar, and it doesn't quite solve your problem, let me know, I can probably do a short video of this sequence and post it later tonight.