To open and close clickers / segment rings / hinged segment rings, gently spread apart the ring slightly and flip the segment open / close.
Many people find it difficult to open small pieces of jewelry, since the rings can be small and difficult to grip.  There are some simple tricks that you can try :
1 - we carry opening pliers for body piercing - https://rebelbod.com/collections/body-piercing-tools
2 - Home Depot has generic all-purpose opening pliers. These pliers basically spread the nose apart when squeezing the handles. Regular needle-nose pliers are awkward to use - you would need to spread the handles apart to spread the nose apart.
3 - slide the lever of a nail clipper or something similar thru the ring, and apply slight pressure to pop the ring open. Position so that one side of the lever is pressed against the opening of the clicker, and the other end of the level will leverage against the non-opening side of the clicker. If you can't tell which end of the segment is the opening, then position in the middle of the hinged segment. It's basically to use the lever to spread the ring apart slightly.
4 - take a hair pin and place the ring in between the hair pin so the hair pin can pull the hinge segment open with the looped end of the hairpin. This method can be used too once you have the ring in and need to take it off. If you don't have hair pin handy, you can substitute the hair pin by bending a paper clip into similar shape as a hairpin.
If the clicker is not closing properly after opening, the clicker is probably spread too far apart from opening. Please check that it is now not warped by placing it on a flat surface and make sure the entire ring can lie flat on the surface. Then try squeezing the ring to tighten the diameter and position the little nub into the notch to close.