This tutorial is based on odoo 8.0
The odoo email system is very powerfull but not trivial.
Following a discussion in the odoo Italian forum, I will describe the basic configuration to make the integration work in the most common use case: users will keep using their usual email address but, in parallel, comunications related to odoo documents will be handled and tracked by odoo.
Create a mailbox to be used by odoo, say firstname.lastname@example.org (I tested it with a google email).
In odoo, install fetchmail and configure the incoming and outgoing mail servers (Settings --> Technical --> Email) for email@example.com. If you use google, the SMTP server is smtp.gmail.com (with SSL/TLS) and the IMAP server is imap.googlemail.com (with SSL/TLS).
Configure the system parameters (Settings --> Technical --> Parameters) mail.catchall.alias and mail.catchall.domain with odoo and yourcompany.com respectively.
Create 2 new odoo users using existing email addresses, like firstname.lastname@example.org and email@example.com.
Log into odoo with user1, create a new document, say a customer customer1, and add user2 to the document's followers. Send a message to the document's followers using odoo:
Go to firstname.lastname@example.org mailbox, open the received message and reply to it.
Wait 5 minutes (standard interval of fetchmail cron) and email@example.com will receive the answer sent by firstname.lastname@example.org.
Every message of the thread will now be appended to customer1.