First acquire a good grapefruit. Pink grapefruits are ideal. They should be round in shape, with a bright red flush and should have no indents or sores. You want a nice firm, round specimen.
With a good sharp knife, cut off the bottom of your grapefruit. This will give the grapefruit stability on your cutting board. Remember that the grapefruit is round and round things like to roll away.
Stand your grapefruit on the cutting board, cut-side down. Then run your knife down the sides, taking the peel as you go.
Why shouldn't you just remove the peel by hand you say? Well, cutting off the peel this way will also remove the fibrous tissue from the grapefruit sections. The whole point of this exercise is to get at the delicate fruit within without all that excess.
Once you finish going all the way around, cut off the remaining pieces of peel on the bottom of the grapefruit and any pieces you missed.
Now take a paring knife and cut into each section along the fibrous tissue wall that separates the sections. Run the knife along the inside of one side and the other and scoop out the flesh. This is tricky and will take lots of practice but it is well worth it.
Once you have gone all the way around, throw out the fibrous middle section. Now you have delicate and delicious sections of grapefruit. These work well in a nice fruit salad. I like to eat the sections as they are with a little sprinkle of Splenda or sugar. You can also use this same method for oranges. Enjoy!