My ring went down the drain!!
This is a messy but usually uncomplicated task that requires:
-Pail or basin
-Scrap rags or paper towels
-Two large wrenches or pliers
-Flashlight or trouble light-depending on your vision and the time of day
I say “usually uncomplicated” because, especially in older homes, materials may have become brittle or dried out with age. Older homes also suffer from the skills of “home handymen” who fix things with electrical tape, use silicone caulk when they don’t have the right gasket and produce other creative “solutions”.
With the light arranged so you can see what you are doing and your hands are free, the basin under the trap, and the rags within easy reach, use the pliers to loosen the plastic or metal nut on both ends of the trap (photo). If the trap is a newer plastic one a single pliers is all you should need. However, if the nut is hard to loosen, use the second pliers to hold the trap in place while you twist the nut loose. It is not good to twist the entire line while you are trying to get the trap loose as it can cause leaks and problems elsewhere.
As the nuts loosen the water in the line will start to leak out and begin to run down your arms and/or into the pail. Loosen as much as necessary to get the trap to come off in you hands. MAKE SURE YOU REMEMBER EXACTLY HOW THE PIECES FIT BACK TOGETHER. Which way to the washers go in? Lay things out on a paper towel or rag in the order and position from which you removed them. Check out the inside of the trap looking for anything that may be blocking it. Run some water into the sink and see if it comes through like it should.
Look up inside the tailpiece (part coming down from the sink) and see if you can see any obstruction. The pop-up assembly in bathroom sinks frequently will collect hair balls which should be removed. If all the above are clear the problem must be on the other side of the trap. With the trap removed, you can easily run a snake down the line and clear any obstruction there.
Reassemble the trap using new gaskets or washers as necessary. Some Rectoseal, a non-drying Teflon based joint compound on the threads will make them slippery and help them go back together without leaking.