When I was trying to break in about ten years ago I started by going to some conventions and just trying to meet people. There is the Flashback Horror Con in Chicago, as well as the Wizard World Comic Book Convention, Gen Con down in Indianapolis, Cinema Wasteland in Ohio, and many others. I would recommend just introducing yourself to people and not pitching scripts. Relationships are important because a director/producer/distributor needs to know you are easy to get along with and reliable before they commit to you, because the screenwriting process can be a few months to a year of collaboration (and then another year or so of production which might include some rewrites).
At some point they will want to know you have skills but frankly it is rare for someone to buy a spec script, in my opinion. I have written a few over the years but in the last ten years I have been hired to write 20 scripts and none of them were from my script ideas. Most were rewrites of somebody else's script (that includes Sex Machine) or written to somebody else's specs, either what the director wants or what the distributor wants or so on. I think it has nice to have some to show you know the basics of screenwriting, structure and terms and so on. I use Movie Magic Screenwriter but many others like Final Draft and there is the free Celtx which is a good platform if you don't want to spend money yet.
I hope this answers your basic question, but feel free to write back if you have more questions. I am at email@example.com.