My scriptwriting process for my current short film has been pretty intensive, and rewarding.
The way I started was I jotted down all the notes on what I actually wanted to happen. Then I thought further about where I wanted my short to end, which helped develop the beginning and middle giving them a place to go. I then drew arrows leading up to what I wanted things to lead into.
After I had that outline fixed up I wrote out an actual script, and moved onto my storyboard. Storyboarding is almost a bad word to some people because it's a lot of work, and most people think they can't do it because they aren't artistic.
I'm a big believer in the idea that you MUST have a story board to make a film like the one you see in your head. The way I did mine, was I read through the script and drew every shot that came to mind. I like doing it this way so I don't forget a shot on location, and if things change when I get there, then that happens, but atleast I'm prepared.
You don't have to draw out every shot. Film making is non objective so whatever works for you is how you should go. You don't need to draw things, a popular way to make storyboards is to act it out with friends and just take iphone pictures.
Remember: Failing to plan is planning to fail!