Understand that when you finish a script you are not done writing it. There are always going to be things to change, so falling victim to immediate gratification will only hurt you. Wouldn't you rather send in a 100 percent-completed script with a few revisions instead of a 70 percent-done raw script?
Get coverage on your script. I offer coverage services and there are numerous ones you can find on the Web. Coverage is a critique from very professional analysts. It helps pinpoint problems instead of just "that was bad."
Research producers and companies. Just because you like a producer does not mean he is right for your film. Find out what genres certain people and places specialize in.
Find out if they accept unsolicited scripts. This refers to a script not referred to them by an agent, actor or someone else.
If they do not accept unsolicited scripts, do not send it to them or call them to ask if they can make an exception--move on!
Post your script on websites such as Inktip, which constantly receives hits from industy professionals.
Post something on a website like IMDBPro. Professionals and nonprofessionals alike are on those message boards and may even be able to help get you in touch with those higher up.
Try to secure an agent. If you can nab an agent, then they will take care of marketing the script.