when you see someone with good looking form, you’ll know it.
If you have someone tape you as you run, you’ll immediately see a lot of errors if you have bad form.
and the “arms down” thing mostly applies to a lot of girls who like running with their hands almost pinned up to their shoulders. Also, it applied to me, before my coaches told me to stop doing it. Now, i swing them so that my wrists are almost by my hips at the bottom of my swing, and my fingertips are about level with my shoulders at the top, but my elbows are almost locked into a 90 degree angle throughout my whole stride. the “swinging forward, not across” is a common problem though, and something a lot of coaches will look to fix. One trick is they’ll have you pretend you’re holding guns and you’re looking to shoot someone in front of you. If your arms are swinging too diagonally, you’ll obviously miss your target. Also, another (or so i’m told) common problem is having your shoulders up by your ears and really tight. That constricts your breathing, and wastes momentum. that’s another thing people mean by “arms down”
something else to take note of: your feet. if you go into a running shoe store (especially a good one), the salesmen always want you to try the shoes out at a running pace, and watch your form. If you’re wearing the wrong type of shoes, your form will suffer, and ultimately your whole body.
Another important note: your form should change based on terrain.
For example, when climbing up hills, taking shorter strides, driving with the knees, and swinging with the arms more is not only natural, but more efficient.
On downhills, taking long, bouncy strides happens, and you can gain a lot of ground if you do a sort of “windmilling motion” with your arms and lean forward with the hill (it’s scary to lean forward with the hill, but the arm motion-which happens naturally for most people-will keep you balanced.) if you have knee or shin problems, i don’t recommend pushing the downhills like this. It really does wreck your knees, and shin-splints will feel a lot worse.