Move away from blogger. How to?

Hi,
I have my own blogger site (http://mindfulmimi.blogspot.com but have just acquired my own domain name. Right now these two stand side by side and blogger the dot com address is redirected to the blogger one. I want to avoid this duplication as also google does not like this.
But I am puzzled as to how to go about.
I have read all the how to's on moving from blogger to wordpress etc. But is that not just trading one free service for another?
Do I first need to find a web host and copy my site onto their servers? and then delete the blogspot? And is that possible without loosing data, comments etc and google ranking?
I just want to use my mindfulmimi.com address without having any link to the blogspot anymore.
Is there a simple tutorial for that?
Thanks