Cut the the two "poles" off of the grapefruit. The top and bottom, not through the middle.
Now you have a flat base to work with. Using the sharpest knife you have, (my pairing knife is my go to for this situation) cut off the peel in sections, allowing your knife to glide along the fruit, moving all the way around the grapefruit. Go back and cut off any remaining bits of pith.
The white pith of grapefruit is bitter, which is the white layer between the outer peel and the flesh of the fruit. By peeling the grapefruit using your knife, you'll get rid of all of this.
On to segmenting the grapefruit so you have nice little pieces! Glide your knife into one segment of the grapefruit as close to a membrane as possible, and make a slit on the other side of the membrane.
Now you've made a clean cut, and can loosen the segment of fruit with your knife, popping it out in one piece. (Think of this process like removing pages of a book, in between the covers.) Do this around the grapefruit and you'll have perfect segments.