To install one of the tar packages download it to a suitable location,
start a terminal application, switch to that directory and issue the
following:

$ tar xf opera-next-12.00-1256*.tar.xz
$ opera-next-12.00-1256*/install

After install you should find an "Opera Next" entry next to "Opera" in
your program launcher, though it may be necessary to log out and back
in to your desktop environment again.

Note: If you are having problems opening the tar packages, please read:
http://my.opera.com/ruario/blog/2011/11/26/xz-compressed-snapshots