There are many reasons to want to have your child be able to swallow pills: to avoid the taste of liquid medications your child may not like, to avoid spilling liquid medications, to make it easier to carry the medicine with you, and to avoid having to buy multiple forms of over the counter medications.
We meet young grade schoolers who can swallow pills and teenagers who cannot swallow pills. There is no magic age where "you should be able to swallow pills" but the average child learns to swallow pills at about 11-13 years of age. Many children can start to take pills aimed at adults when they reach more of a petite adult size (85-100 pounds). Check with your doctor's office about specifics for fever reducers, cough and cold medicines, and antibiotics.
Drink something: Every pill we would recommend for or prescribe to your child can be taken with something to drink. For many children trying to swallow a pill, having something to drink before and after helps tremendously. Take a drink and swallow first. This makes it less likely a tablet or capsule will feel more "stuck to your tongue" and more likely it can "slide down" well. Then pop the pill into your mouth and quickly follow that with a good-sized drink to "wash it down". If the pill did not go down, follow it with a few more swallows of something to drink.
Mind where you put the pill in your mouth: Some folks find it helpful to "toss the pill back" as far as you can on the back of your tongue -- closer to where we want the pill to go. My partner Dr. Jeff Crecelius often advises tossing the pill onto your tongue, taking a drink of something and briefly hold it in your mouth, tuck your chin to your chest, then try to toss your head back and swallow at the same time. The idea is that this motion as well as the swallowing the liquid will propel the pill back so that it is easier to swallow.
Practice with something small: Small bits of candy are a good way to practice. One of my sons liked starting with Nerds(r) candies. He would try those one at a time. If they went down easy with a drink or two of water, we moved onto something a little bigger: TicTacs(r) or M&Ms. If you can swallow one of those with water, you can swallow a reasonably sized pill. The good news is that if your child does not swallow the pill, they can always chew up the piece of candy and try again.