Think steam locomotive:
Everything should be going in the direction you want to travel. So your arms will help you most when moving forward, and not side to side or over-extending in front of your torso. Keep your shoulders relaxed, arms loose and try not to bend at the waist. With the exceptions of sprinting and running uphill, your hands shouldn’t pass behind your torso during the swing back, and your elbows shouldn’t come to the front of your torso during the forward swing. Uphill running involves driving your arms high in the air by your head to aid in forward, and upward momentum. During uphill running your arms are doing a lot of the work to drive your weight up the hill.
Let your hands be calm and unclenched. The old adage is to pretend you’re holding on to a butterfly or a potato chip with your thumb and index finger, nice and loose. Tight hips impede leg swing, and effective gait. Keep ‘em loose as well and flow during your run!