To open or close a jump ring, its easiest to use two pairs of needle nose pliers.  If you only have one pair, you can hold on side with your fingers. 

If there is a gap, close it by moving the sides up and down pressing gently together.  The ends should slightly overlap then snap together tightly so the tension of the metal will hold the gap closed.

When you oopen a jump ring (or any loop) twist it open rather than pulling it open so it will hold tight when re-closed