This is not for occasions when you can't breathe! That would require the Heimlich Maneuver or a tracheotomy.
Occasionally, a piece of candy or a potato chip - even a large ice cube - can slide down into your throat before being chewed. Given time, most food will dissolve on its own. Meanwhile, this does hurt. Run the water from the tap until it is pretty hot (but not hot enough to burn) then fill a small cup with it. Drinking the hot water will dissolve stuck foods such as these, and one swallow may be all that is necessary. A few more sips will help be sure that the food can get to your stomach safely and without pain.
When trying to dissolve the stuck food doesn't work, taking a few big drinks might help. Or, swallowing a rather large bite of something really substantial, like a burger, to push it down. Sometimes a piece of food goes slightly up the back of the throat so swallowing doesn't reach it. For that, you could try taking in a large amount of water and not swallowing, instead swish it around in your mouth while pointing your head up then down so the water might reach the food. If that doesn't dislodge the food, you could try to reach it with your finger or toothbrush.
Sometimes the piece of food might be up so high that it actually has to come out your nose. That would take a lot of blowing or snorting, and having food come up through your nose feels really gross.
If nothing else works, what you feel is probably not food at all but an injury from food that was hot enough to burn that area or hit just right to scratch that area. The best thing to do for this is to gargle with salt water, a little hydrogen peroxide in water, or a tablespoon of honey in water. All three are good germ killers so your throat won't get infected, but the salt water might hurt.