What you're about to read is definitely a Cole's Notes answer. It's a question I get asked every so often, but my response is always the same. I'm sure others do it differently, but this is my routine. For me, every project I've ever started got going with a plot point or situation. Never have I started with a character. I've spoken to some writers who've been inspired by character. I'm not one. Every single thing I've written has started like this and I don't see myself changing anytime soon. Why? Because it works for me. I will add that in the end, to have a successful story you do need both plot and character, but for me, when I start, it's always been plot based.
Once I have the initial plot point I want to explore I then ask myself how do I want this story to end. Once an ending has been conceived I then work in some characters. I'll start asking myself 'what if' and before I know it, I'll have a list of characters, not yet fully developed, but ready to be tossed into this hell I'm about to dream up. After I have some characters, I'll work on developing them a bit further, and by that I mean giving the main characters some internal and external conflict. After all, movies need conflict. Without it, you have nothing. If you plan on writing a script without conflict don't. Just save your time and go write greeting cards.
After I have a good group of characters, and a plot that has an ending I'm happy with, I then begin with building ACT 1. For those newbies reading this ACT 1 introduces everyone and is known as the 'setup.' After I've introduced everyone and have given the audience all it needs to know about what the movie is trying to accomplish, I then proceed to plotting ACT 2 - confrontation. Basically, in ACT 2 what you're doing is tossing crap at your main characters, and if they're somehow able to dodge it, you then drown them in crap. The whole point of ACT 2 is to push your main character to his/her limit. After you've tested your main character(s) though out ACT 2, you're then off to ACT 3, or otherwise known as the 'resolution.'
ACT 3 is your story's ending. This is where you need to wrap everything up and more often than not, have some sort of happy ending. Again, the most important part of writing is knowing what to write. I accomplish this by plotting out every scene on 3 x 5 cue cards. Why cue cards? Because you can easily change, or re-organize them if something doesn't work. It's simple. You have a blueprint of your story in front of you, and once you're done plotting your entire story on cue cards, all you have left to do is actually write. Not so hard sounding is it?