A lot of scenario in my mind with "free" things around domain, hosting and email which is DNS.

There is many provider offer DNS management for free like :

• zoneedit
• mydomain
• dnsexit

these provider offer dns management that you can use for  :

1. Hosting your blog for free at awardspace, pointing your email at google apps plus other facility in google like gtalk etc.
2. Hosting your blog in your own server, pointing your email at google apps
3. Hosting your own email with free hosting from awardspace or other free hosting

Off course first scenario is the best, only need domain to start

Wait, if you wanna free domain then you can check out this thread :

"Win a year’s worth of hosting at BloggingTips.com"

Make sure to prepare yourself to win by reading this article :

• The Basics of Hosting a Blog
• Step by step to get your own email in google apps