The best way to get faster at assembling a puzzle ring is to find instructions online and practice repeatedly until the movements are natural and simple to do. Puzzle-Ring-Solutions.com has 10 different videos showing the solutions for different puzzle rings. There are many different varieties, but they all have similar solutions. Once the motions for solving the puzzle ring are memorized, repetitive practice makes the process much faster.
Do not use force to assemble a puzzle ring, because the bands may bend, preventing the ring from assembling correctly. Without instructions for the specific puzzle ring that needs to be solved, the solver must expect some trial and error in learning to solve the ring quickly. Websites that sell puzzle rings are most commonly visited by people looking for a solution to their puzzle ring, so many such websites offer general tutorials, videos and step-by-step instructions on how to solve a puzzle ring. JohnRausch.com and PuzzleRing.net have written and visual instructions that can help owners learn how best to solve the rings they own. Different methods may be easier or more difficult, depending on the ring, so finding the simplest method for the puzzle ring in question allows owners to improve their solving speed.