Of all the drains in your house, the sink drain is the easiest from which to retrieve a stuck item. The sink gets used a lot, so its drain is the one in which stuff is most likely to get stuck. The shower drain and some bathtub drains have strainers that prevent all but the smallest debris from getting in. However, many bathtub drains are either left open or have stoppers that leave a gap through which an item as large as a ring can easily fit. As far as the toilet is concerned, it can easily swallow up a large item, such as a stuffed toy.
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Plunging out Clogs
If the obstacle is causing a clog, and you don't want to retrieve it, you can usually plunge it into the waste system, where it is lost forever. If the item is valuable, however, and you want it back, you can't take such a cavalier approach. Your retrieval efforts should focus on the drain P-trap, because that's where the item probably is.
Something Stuck in Sink Drain
The sink drain may be the one in which stuff is most likely to get stuck, but fortunately, it's the one from which it's easiest to retrieve stuck items. All you have to do is disassemble the P-trap. This procedure is simple, and you can usually do it by hand, but you may need a pair of adjustable pliers.
Unscrew the compression nut at the mouth of the trap, lower the trap and swing it away, then unscrew the nut at the exit of the trap, where it meets the trap arm, and pull the trap off. Do this carefully, because it's full of water. Invert the trap over a bucket and out will come all the water along with all your valuables that have collected in the bottom. If the item you're looking for isn't there, and the drain is still blocked, don't despair, because there's still something you can do.
Unscrew the trap arm from the waste inlet and look inside the arm, then probe the waste pipes with a piece of wire or a zip-it tool and try to hook onto it and extract it. If you can't dislodge it, fit the hose of a wet/dry vacuum over the waste opening, seal the connection with tape and turn on the vacuum. You'll probably get a lot of gunk, but you should also get what you're looking for.
Something Stuck in Bathtub Drain
Unfortunately, you can't access the bathtub P-trap without demolishing the ceiling underneath the tub. You may want to do this if the item you lost is valuable, but you might not have to if you can vacuum it out or use a telescoping magnetic tool to get it.
First, you have to remove the stopper or the strainer, and while the procedure depends on the stopper mechanism, they are all removable. Try hooking onto the item with a zip-it tool or, if it's metal, latching onto it with a magnet. Vacuum all the water out of the P-trap as a last resort, and once you remove the obstruction, remember to run the water to refill the trap after you replace the stopper or strainer.
Accessing Shower and Toilet Drains
You can use the same procedure to remove something stuck in a shower drain, although, because the strainer keeps out all but the smallest items, the zip-it tool is probably all you need. The item, whatever it is, is probably surrounded by hair, and the zip-it tool is very good at latching onto hair.
When something is stuck in the toilet P-trap, you can try putting on gloves and reaching into the P-trap to get it. If you don't have any luck, use a toilet auger. As a last resort, take the toilet off, turn it over and reach in from the other side.