You need superuser (root) access on your Ubuntu box to install it in the root directory.
I'll assume you have that, so open a terminal as root, change to the root directory and unpack the archive using the 'tar' command:
Code:
# cd /
# tar -xv --strip-components=1 -f /path/to/bitcoinUnlimited-0.11.2-linux64.tar.gz
You should see the files being extracted.
Close the root shell, and log in to your regular user account, create a .bitcoin subdirectory in your home directory.
You should be able to run the "bitcoin-qt" program, assuming /bin is in your PATH.
If not, you are probably still missing some packages on which the Bitcoin client depends.
You should see some error messages in that case though - please report them if you do.
About the script above: I pointed you to that not in order to simply run it, but to look at the commands it performs, to get an idea of what you might need to install on Ubuntu in terms of prerequisites.
Of course, it's geared to compiling a Bitcoin client from source, but some of the instructions might still be useful in general.
I'm sure the BitcoinUnlimited project will provide better links to information soon.
Bitcoin Unlimited builds largely on the same code that BitcoinXT and Bitcoin Core does, so they have very similar installation requirements and procedures.
Surprisingly, the page at
https://en.bitcoin.it/wiki/Help:Installing_Bitcoin_Core does not have any information on installing on Linux in general or Ubuntu specifically. A difference in Bitcoin Core is that there is are
Ubuntu packages for it, making it a bit easier to install.