update: jessie is now at ftp.au.debian.org too
ftp.us.debian.org now has a copy of jessie, even though ftp.au.debian.org still doesn't.
This means that you can switch to the new testing (jessie) by editing your /etc/apt/sources.list:
deb http://ftp.us.debian.org/debian/ jessie main contrib non-free deb http://www.deb-multimedia.org jessie main non-fre
At this point jessie is simply a copy of the 'old' testing, wheezy, so if you've got an up-to-date wheezy there are currently no updates involved in switching to jessie.
If I've understood things right sid was frozen at the same time as wheezy, so that it will take a little while before changes will occur in jessie since they first need to be introduced to sid, and then filter through.
Note that once updates start flowing into jessie the odd breakage might occur, so make sure to install apt-listbugs to get warnings about known bugs.
Upgrading from Squeeze to Wheezy
Upgrading from the old stable to the new stable is simple enough.
First make sure that Squeeze is up to date
sudo apt-get update && sudo apt-get upgrade && sudo apt-get dist-upgrade
Edit /etc/apt/sources.list and replace all instances of squeeze with wheezy. Then update, and download all updates before upgrading (-d).
sudo apt-get update && sudo apt-get dist-upgrade -d sudo apt-get upgrade && sudo apt-get dist-upgrade
If you get an error about default-jre you can uninstall openjdk-6-jre and then run dist-upgrade again. It should work.