Everyone has heard about the Heimlich maneuver, which has saved many lives. It basically uses the power of the hand closed as a fist to force air up from under the lungs to pop out the food obstruction using the force of the expelled air. But here is something one must consider in addition to knowing how to do this maneuver.
Sometimes the food obstruction just moves a little ways up and then falls back down into the place where it was stuck. This is especially a danger with children. Heimlich maneuver is also problematic with small children because it is easy to break a bone or other organ when trying to do as energetic a rescue technique as would be all right with an adult. So what you need to do for both children and adults is to remember to let gravity help with the rescue.
When trying to rescue a child from choking be sure that they are positioned so that they are head down far enough so that basically when the food is dislodged it will fall out of the mouth to the floor. So literally tilt the child upside down while doing either the slap on the back technique or the child version of the Heimlich. One easy way to do this is to bend the choking victim over the back of an upright chair, so that their head is near the seat. When the food is dislodged, through either slap on the back and victim coughing or by child version of Heimlich maneuver, the obstruction will pop out and fall out of the mouth, rather than risk falling back in.
I actually once tended to myself this way when having severe choking. Living alone I had no one to help so I bent over a chair while coughing and hitting myself on the back and was able to dislodge the food.
By the way, this reminds me of another important safety reminder. I remember seeing someone tend to a hurricane Katrina evacuee who was laying on the floor of the evacuation collection location, I think the airport. The person was parched and needed water and the tender gave the person water without lifting their head! I almost fainted. A person cannot drink or eat while laying flat on their back without risking choking. It's not sentimentality when we see in the movies the hero lifting the head of the injured person to give them a drink of water. The head must be raised in order to keep the food or water from going down the windpipe and causing choking. So do not under any circumstance let an ill or disabled person eat or drink without lifting their head (unless your physician or caregiver has made other arrangements). Never let your children mess around and eat or drink while laying flat on their backs.
I sometimes despair of how much simple medical and health knowledge that used to be common sense and common place is unknown now. It is not only true of the average person but also "medical professionals." Some years ago I went to a "Park Avenue" gynecologist after mine had retired. This doctor was a young woman and recommended by a woman I worked with whose daughter went to her. After the exam I mentioned that I had a sore throat (I think it was around cold and flu time) and she volunteered to take a look. So she told me to open my mouth and stick out my tongue. I did, expecting her to turn to her supplies and pull out a tongue depressor. But she said, "Your tongue is blocking my view, lower it!" I was dumbfounded. I tried to do so but of course one cannot since the muscles do not allow that (that's why tongue depressors exist, duh). She got snippy with me and said, "Well, if you are not going to lower your tongue then I cannot see in your throat and do the exam!" I could not believe it, this is a DOCTOR and she clearly did not know that one has to use a tongue depressor. So I used my finger, can you believe this? I used my middle finger as a makeshift tongue depressor. And watching her face I honestly do not think she knew that you had to use that odd little flat piece of wood gizmo to hold down a patient's tongue when examining the throat area. I cannot believe that anyone who has ever been to a doctor (say nothing about actually being one) does not recall that a popsicle stick type depressor is used to push down the tongue while the doctor tells you to say, "ah." So I'm amazed at how lacking in common sense knowledge has been passed along to this past generation both in general and in the "health care services" sector.