Cultivating the ability to "chug" liquid helps enormously.
Incidentally, before you start mashing/cutting pills up, some prescription medications or time release OTC meds are not meant to be dissolved or otherwise broken up before swallowed, so you need to check with your doctor/pharmacist about that.
To swallow a pill that is not a capsule, put it in your mouth as far back on your tongue as you can. Take a large, but not monstrous, mouthful of water (don't take pills with anything other than plain water). "Toss" the water back into your mouth quickly and swallow with your head tilted up, nose pointed to the ceiling.
With capsules the swallowing process is in reverse (tilt your head downward a little, nose toward the floor) as capsules float.
Don't overthink the process, and don't hesitate with the pill in your mouth too long, it gets stuck to your tongue and that ruins everything. The trick is to learn how to swallow a large mouthful of water quickly, first, and then learn to toss the pill in your mouth and take a quick gulp of water and wash that bad boy back fast.