This is how I updated my personal blog (www.nowhereland.it - ita).
My blog is located under the blog/ directory.
First of all (optional) I’ve put an index.html under blog/. This index.html looked like this page which is saying “the site is being updated, please stand by, blah blah” :P also I’ve renamed index.php to index.php- so that it was temporarily disabled
Then I’ve created a blog_2 directory where I’ve uploaded the fp package.
I finally moved my /blog/fp-content/ to blog_2/fp-content/ 
Now you can already test if the installation under blog_2/ works, just browse to http://mysite/blog_2/
Some content may look weird: your entries may be ordered from older to newer: this is because the caching method changed from 0.612 to 0.703 (and this is why I suggest you (1)to upgrade, and (2)to upgrade using this method :)): just empty your fp-content/cache/
If you have still issues (but you shouldn’t) use the maintenance tab in your control panel or re-install
Finally, rename blog/ to blog_old/, blogxxx/ or something
rename blog_2/ to blog/
You’re done :)
Now if you encounter any big issue, repeat the procedure in reverse (always empty the cache) and you’re back to your old fp installation
And don’t forget to report your bug!
 Please notice that this may not work the same in our next releases.