Your goal is to have the rings closed so perfectly that you cannot feel the joint (unless your rings have burs from their manufacturing process) and you can only see the joint if you look very closely with a magnifier.

How to close a ring perfectly: To do this, twist the ring one wire-diameter past the point where the wire ends meet. While doing this, push the ends together twice the amount of the gap (kerf). So, with a pair of pliers in each hand, grip the ring firmly (but not too tightly or you'll leave tool marks) covering almost half of each side of the ring with the pliers with the ring opening toward the tip of the pliers. Then, you'll simply rotate the pliers slowly while pushing their tips slightly together (to create a "click-click" sound--more on that later).

Pushing the ends of the pliers together closes the gap (kerf) made during the manufacturing process of the rings. This creates tension in the ring that will help keep the gap closed and make the product stronger and prevent the ring from snagging on clothing.

Note that this is difficult to do with armor-grade (steel) rings because they are strong and require similar strength in the artisan to achieve this close of a meeting between the ends. Fortunately, it is much less critical in armor than in jewelry.

Then, twist the ends back together until they meet perfectly. The spring tension should hold the gap where the ring was cut together and your over-twist should should keep the ends aligned in a perfect circle.

Once you've mastered this technique, you will hear a tell-tale "click-click" sound as you rotate the pliers forward and back, indicating that the spring-tension will securely hold the ring perfectly closed. It may take weeks and several projects to master this, though, so don't panic if you don't hear this clicking sound immediately.