It's best to grip the jump ring across as much of one side as possible. This gives you maximum control when using the other plier/hand to open the other side. Pull the other side towards you. Don't open the jump ring by pulling the two sides apart in opposite directions. Doing this will bend the ring out of shape!
Once you have used your jump ring, close it back up again moving the ring back into shape.
To strengthen the ring and ensure it is tightly closed up push the two sides gently together whilst moving them back and forward.
And that's how to open and close a jump ring. Don't worry if it seems a little tricky at first. It takes a bit of practice to make perfect, but I promise after a little time you'll be making perfect jump rings automatically!