Fill/email LiveCycle forms in Reader?

Yes, this can be done. First you'll need a script for sending form by email using email addresses entered on the form.
Read this Article:
http://www.acrobatusers.com/tutorials/form-submit-e-mail-demystified

In it you'll find a link to another article on exactly this topic. But read this article first.

Next, in order for you users, and thier users to be able to email the entire form, the PDF will need to be Reader Enabled for Save. In Acrobat Pro 8 this option is on the "Advanced Menu"

Thom Parker
The source for PDF Scripting Info
[url=http://www.pdfScripting.com]pdfscripting.com[/url]

The Acrobat JavaScript Reference, Use it Early and Often
[url=http://www.adobe.com/devnet/acrobat/javascript.php]http://www.adobe.com/devnet/acrobat/javascript.php[/url]

Then most important JavaScript Development tool in Acrobat
[url=http://www.pdfscripting.com/public/34.cfm#JSIntro][b]The Console Window (Video tutorial)[/b][/url]
[url=http://www.acrobatusers.com/tutorials/2006/javascript_console][b]The Console Window(article)[/b][/url]

I don't think this is quite the answer I am looking for. I looked at the tutorial, maybe I am in way over my head. This is the first form I have ever created, so I'm quite new to this. Someone did tell me that I had to make my PDF "reader enabled", but as for needing a script. I guess I don't understand what a script is or where to put it or how to include it for that matter.

My situation is a little different here because I can't add the email addresses on the form. There will be various businesses accessing this form (these addresses will always be changing), they will fill it out and then send it to various companies. I will never have knowledge of the email addresses they will send to, nor can I keep track of the people accessing this form.

Now that I have explained it a little more in detail, do you think there is still a way to do it? I did make a form and email it out to test, but the receiver could not fill it out or send it by email to someone else. I am thinking that maybe you cannot do this.

Yes, I know exactly what you are asking for and the answer is in the articles. The article I provided the link too is all the general concept of submitting/emailing forms.

In that article is a link to an article on setting the email address dynamically, and it has an example file that shows exactly how to do it.
http://www.acrobatusers.com/tutorials/dynamically-setting-submit-e-mail-address

And this is the bit that requires a script. Dynamically setting an email address is a custom activity. All custom behaviors require a script of some kind.