Not speaking from success but what I've heard.

- Start querying prodcos, etc. You can get contact info through IMDBPro.
- Maybe subscribe to Inktip for a few months to get that lead info.
- Enter some reputable/valid screenplay competitions.
- Network with people (like you do here) and pray a friend of a friend of a friend actually has some connections.

Keep writing more screenplays or look at Inktip for a request for one you might be interested in writing and reply to it with a pitch and write that script like mad!