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Choose a small auger that is made to snake sink drains. Gather the additional supplies you'll need. Remove the P-trap in order to access the drain pipe. Push the auger cable into the pipe coming out of the wall. Turn the handle on the snake to break up and grab the clog. Pull the snake out of the drain slowly. Put the P-trap back together. Test the drain by running water down it.
Small sink augers are hand-held tools that have a handle and a round compartment that houses a spool of wire with a corkscrew-like tip. They are often called "drain augers" and are available at all home improvement and hardware stores. There are several types of augers that are commonly available. Choose one that has the round compartment on it, as these contain enough wire to get down into your drain. There are augers with shorter wires, which are called closet augers, but these are made exclusively for snaking toilets. In order to snake a sink drain, you will need a bucket, towels, a wrench, a screwdriver, and gloves, in addition to a snake. The bucket and towels will help you keep your sink area clean and dry while you work. The wrench and screwdriver will help you take apart your drain if it becomes necessary. Wearing gloves while you work on your drain will help to keep your hand clean and will help prevent injuries from occurring. Use your wrench or screwdriver to loosen the slip nuts on both sides of the P-trap. Once they are loose, you should be able to pull off the P-trap piece with just a bit of wiggling and force.  The p trap is the curved piece of pipe directly under the drain on your sink. Its purpose is to keep sewer smells out of your house and to catch debris that might get lodged further along in your pipes. Place a bucket under the sink to catch water and other debris that will pour out when you detach the trap. Some P-traps require a screwdriver to remove and some require a wrench. You will know which you need by looking at the attachments on the P-trap under the sink. Push it in slowly and keep pushing until you feel strong resistance. When you do feel resistance, pull the wire back just slightly and then try pushing it in again. If you are hitting a turn in the pipe instead of a clog, you may be able to get past it by pushing it through again. In general, a bend in the pipe will give your wire a complete and solid stop. On the other hand, hitting a clog will feel a bit spongy. Once you have hit a stopping point, its time for the corkscrew at the end of the wire to do its job. By turning the handle on your auger you will turn the wire in the pipe and hopefully dislodge some of the clog. Additionally, you may hook the clog onto the end of the snake.  Turn the handle slowly. You don't need to move the snake quickly. Keep pressure on the snake as you turn it. Pressure on the wire will help push the corkscrew end into the clog. If you have successfully hooked the clog onto the end of the wire, you want to keep it hooked so that it can be removed. To make this happen, be slow and gentle as you remove the wire.  If you can feel a slight sensation of resistance on the wire as you pull it out, that is likely the clog hooked onto the end. If the end of the snake has a clog attached to it, move on to putting the drain back together. However, if it doesn't, push the snake back down the pipe and try to hook it once again. Once you suspect that you have removed the clog you can put the P-trap back in place. Put it in its original position and retighten the nuts. Keep the bucket under this area of the drain pipe so that if there are any leaks while you are testing the drain the bucket will catch them. Run a steady stream of water down the drain to determine if you have cleared out your pipe. If the water starts to back up, turn off the water before it fills your sink.   It may take a few seconds to clear out debris in the pipe once you start running water. However, the water should begin to run freely pretty quickly if you have dislodged the clog. If you still have a clogged or slow drain, you can either try to snake the pipe again or call a plumber.