It is important to remember that the human brain “stabilizes” the image that appears on the screen during filming. As we acquire the footage, our eyes will naturally fixate on some landmark and track it along, giving us the false impression of smooth camera movement. We’re often surprised to find extraneous motion upon subsequent review, as if we had been filming from atop a trotting horse!
When possible, keep the phone close to your body, rest your elbows on a nearby object and use your body (not your arms) to absorb bounces and shakes. Most of us do not have access to a tripod, so lean against a wall if there is one available. That’ll help keep the shakiness to a minimum. No wall? Put your butt on the ground, bend your knees, and prop your elbows on them. Presto: instant tripod!