What does it mean to have an agent "submit" me? Will it be okay with producers that I'm not officially signed by them? And when I call an agency, will the person who answers be the person I need to talk to or should I ask to talk to the literary agent?
The term is "hip-pocket," and it's when an agent will send in your script (ie: submit you) without actually taking you on as a client. To get signed as a client is a whole big deal; getting someone to submit you to places where you've already made the contact and they are expecting a script from you, that's easy. The agent could be a friend or acquaintance, or simply a contact made by phone. You give them the script, the producer's name and address, and the guarantee that the material they're sending has been requested by the recipient. They stick it in an agency envelope and send it out and voila, you've been submitted by an agent and the execs can read you. You don't need to make the distinction between being signed and being hip-pocketed. They don't care.
When calling an agent -- or anyone, for that matter -- be extremely nice to everyone who answers the phone. Assistants become agents and producers, and besides they have a lot of power anyway. They're the trusted right arms of the Powers That Be, and they can be your best allies.
I would explain the situation simply, but clearly: You have a producer who has requested your script, but it needs to be sent in by an agent. Do they have an agent who would be willing to do that? The answer will be yes or no, and sooner or later it'll be yes. Don't be coy; if asked, tell them who the producer is. The more well-known the production company, the more likely they are to say yes.
Also, be sure to thank everyone who helps you. There's very little acknowledgment in this business, but it's the one thing that will make everyone glad to have helped you out and willing to do it again.
I've emailed many production companies; I just can't seem to get production companies to give my emails a second look.
Ah. E-mails. Easy to send, even easier to ignore. Phone calls are much, much better. By definition, you talk to someone -- and they talk back. So you can find out why they're not interested (if they're not) and what they would be interested in seeing. You may be targeting companies with your e-mails that have decided they're only going to do movies about bunnies from this point forward... You have no idea. A phone call clarifies matters.
That said, the other thing is your pitch. It is just as important as your script, because no one will read your script if your pitch isn't catchy. Try it out on everyone -- friends, family, teachers, fellow writers -- to see if they 1) get what your script is from the pitch, and 2) think it's fun, enthusiastic and engaging. You want to be short and jazzy. For instance:
"Elephantitis" is a romantic drama about a modern-day woman who's hit by a car while exploring her family's roots in a fishing village in Ireland. She's knocked into a coma, and she wakes up in a Dublin hospital... only the year is now 1872.
Seriously, just that long -- about three lines. Then when they ask questions, be prepared to answer in short, concise sentences. Be sure to tell them it's a completed script. What you want is for them to request it. They'll usually require a release form, which they'll probably e-mail you. You'll sign it and send it in with the script and a cover note, reminding them of your phone conversation. Also, write "Requested Material" on the envelope.
It's a numbers game -- your script will be their cup of tea or it won't. If not, ask what their brand of tea is and keep track so you know who to call with your next script. Again, that's the advantage of a phone call over e-mail.