After looping the cord through the zipper slider or pull (depending on whether you are removing the metal pulls or simple adding the cord pulls to the metal pulls), thread both ends of the cord through the plastic outer sheath of the pull (the part with the hole going through it), making sure the wider end of the outer sheath is furtherest from the zipper slider.
Then, push both ends of the cord into either side of the the inner part of the pull (the part with two prongs with teeth on the inside); you'll have to pry the prongs open a bit with your fingers as you slide the cord ends in - pushing the cords in from the sides is easier than trying to shove them in from the opening of the prongs.
You want to slide the cord ends all the way in between the prongs so the the cord ends are flush or nearly flush - if you try to stuff too much cord in, the outer sheath won't close onto the inner pronged piece all the way; if you don't push enough cord in then the teeth won't have enough to bite on to and the cord end might slip out. Make sure the ends of the cord don't stick out of the sides of the inner prongs.
After you've inserted the cord into the inner part of the plastic pull, align the inner part with the opening of the outer sheath and pull the cords back through the outer sheath, in the process locking the inner part inside the outer sheath and locking the cord ends securely inside both.
It may take an additional hard yank to get the inner part to seat fully into the outer sheath; if it won't seat it's usually because a bit of the end of the cord is extending beyond the inner prongs - sometimes you can successfully use a bent-open paper clip or similar to push the excess cord back into the prongs to get the whole thing to seat securely.
If you've been successful in assembling the cord pull but discover you want to remove it, you can just cut the cord off and throw the pull away, or you can disassemble the pull using a small screw driver to pry the top end of the pronged part back out of the outer sheath. Be careful not to jam that screw driver into your hand when you try this.