This is more of a to-do list, rather than a guide. This is what I did, and I know there are easier and faster ways out there in the internet. So go Google for it!
This is an incomplete (and somewhat outdated) guide. Check out How to Deplo fat_free_crm on Heroku (circa August 23 2011) .
If you did everything to the letter (set up Heroku, did a heroku create and git push heroku master), there's a high chance of your deployment to fail.
In fact, if you go to your website on Heroku, you may get this:
What I assume is that fat_free_crm is in constant development, so it may have broken Heroku integration in the process in one way or another.
Fortunately, an alternative is to try out Ryan Wood's version / fork of fat_free_crm. http://ryanwood.com/past/2010/1/21/fat-free-crm-on-heroku/
This particular fork is already configured and set-up for Heroku deployment. All you have to do is heroku create, then git push heroku master.
If you did it right, you should get the Fat Free CRM login page