Acrobat SDK and JavaScript, is the right support forum for what your asking.
You'll probably looking into using the mailDoc() method.
Here's a sample script that I used to help another user recently:
var cFromAddr = this.getField("Email").value;
var cToAddr = "myemail@company.com";
var cSubLine = "I, " + this.getField("Name").value +", " + "want to buy a car from " + this.getField("Range_From").value +" range at a " + this.getField("Range_To").value +" rate." ;
var cBody = "In here is the message body which you can customize and add other text fields as shown in the subject line above." + "\n \nPlease send this email to yourself by clicking the Submit button above, review the terms in this form and save it for your files."
this.mailDoc({bUI: true, cTo: cToAddr, cFromAddr: cFromAddr, cSubject: cSubLine, cMsg: cBody});
I adapted the script with ideas of other users who have posted similar questions and using as a guideline the examples provided in the Adobe Acrobat SDK JavaScript API Reference, Doc methods, page 287.