How to install Opera Browser?
How to install Opera on Ubuntu:
From the terminal, add a pointer to the opera stable sources:
sudo sh -c 'echo "deb http://deb.opera.com/opera/ stable non-free" >> /etc/apt/sources.list.d/opera.list'
Install the key:
sudo sh -c 'wget -O - http://deb.opera.com/archive.key | apt-key add -'
Update repo:
sudo apt-get update
Install Opera:
sudo apt-get install opera
Synaptic is a graphical interface for Aptitude, the package manager in Ubuntu/Linux. It provides a listing of available software packages that are available to download and install from the repositories listed in your Software Sources. Synaptic is less intimidating to use than apt-get in a Terminal interface for users not used to dealing with the command line.
Preceding commands in Terminal/command line with sudo imparts a restricted root-user ability for performing commands that are not available for standard user accounts.
When in doubt about any basic command in Terminal, you can always man [base command] to access the command manual pages. man sudo will show the manual for sudo, for example. There is also extensive documentation on the Ubuntu website for most commands.
As for installing Opera, it is not maintained in the standard Ubuntu repositories. You have two options:
1) add the Opera repository to your Software Sources as mentioned in the other answer and following the directions in the provided link; or
2) download and install Opera manually.
To install Opera manually, go to the Opera website (www.opera.com) and download it from there. Presuming that you have your downloads set to go to your Downloads Folder, you can run the following in Terminal:
cd /home/your_account/Downloads ;ls -l
Replace "your_account" with your short name; the "ls -l" will list the contents of the Downloads folder. Locate the Opera package file - it should be something like 'Opera_12.15.1748_amd64.deb'.
sudo dpkg -i Opera_12.15.1748_amd64.deb and enter your password when prompted. This will run the Opera installer.
In order to have Opera updated automatically, you should still add the Opera repository to your list of software sources.
By the time this question was answered, things have evolved.
By now, you can simply go to Download Opera browser, then click the button above Opera for Windows, Mac or Linux and the website will detect your operating system and processor architecture (32 or 64 bits) using device fingerprinting and prompt you a .deb package to download and install by a simple click using the Ubuntu Software Center.
Update (09/12/2017):
I just tested this again on 2 different virtual machines (Ubuntu 16.04 and 17.04 LTS), and the procedure worked as described above.