>>2884947If you're using just one focal length, get used to it until you can reliably visualize the frame (just imagine a 3:2 box overlaid on what you're seeing). This way, you're already composing before you raise the camera onto your face, and only using the finder for last-second adjustment. Best comparison I can come up with is quickscoping in a videogame.
If you want to be quick with with focusing, use either a camera that will let you manually focus before you're pointing at the subject (Something with a reliable distance scale you can memorize and use by muscle memory like a Leica, or defaults to a certain distance like a Ricoh GR) or something with fast and reliable AF like a DSLR.
For composing with moving, try to guess the general speed and direction they're moving in, and where they might be in relation to one another and yourself when you're going to want to take the shot. (Does that even make sense? It's really weird to put it into words.)
Just keep practicing and you'll get better over time.
