Something that might help is using a very flexible pick. This way, as you develop the technique, the pick will be more forgiving and you can get results earlier. Once you have success with that, you can move up to a stiffer pick.
When I was starting out, I recall using a very flexible pick to smooth out my strumming.
The disadvantage of using a very flexible pick is that the sound starts to sound like a violin with the pick acting like a bow.
Other than that, I would say try to focus on keeping your wrist loose and don't strum from your elbow.
I'm sure that there good tutorials on strumming you can look at. As for what I do, when I strum I find I keep my wrist loose and twist my forearm. There is very little motion in my arm from my elbow.
Hope that helps.