Up to version 12, Opera made their own engine for Opera, called Presto. But 2013, they decided to re-create the browser from scratch, built on Chromium with the Blink engine. The first version of the "new Opera" was Opera 15, and the "old Opera" was discontinued. But as the new browser was built from scratch, it lost many features. Therefore, there are still many users that want to use Opera 12. As it differs very much, there's a second wiki page for that version. You can access it here: OperaBrowser12.
The best and easiest way to install Opera is by just downloading the deb-package from Opera's website. When you install the package, it will add their repository, automatically configured for updates.
When you have downloaded the file, you can install it by double clicking on the file to open Ubuntu software center. If you don't want to add the repository, you can install the package by opening a terminal in the directory where you have downloaded Opera, and run this command:
sudo dpkg -i <opera-package-name>
When you do this, you will be asked if you want to add their repository or not.
You can read more about this here: http://deb.opera.com/manual.html
You can convert the deb package with this script: https://gist.github.com/ruario/8416e36372f1a976a713
Install this package to get flash:
sudo apt-get install pepperflashplugin-nonfree
Java is not supported currently, as they only provide a NPAPI plugin (which are not supported on both Opera and Chrome on Linux).
Get H.264 working
Right now it's a bit complicated to get support for H.264. You can read why here: https://forums.opera.com/discussion/comment/15223803#Comment_15223803
To get support for H.264, you have to run the following commands in a terminal:
sudo apt-get install chromium-codecs-ffmpeg-extra
sudo ln -s /usr/lib/chromium-browser/libs/libffmpeg.so /usr/lib/x86_64-linux-gnu/opera/lib_extra/libffmpeg.so.'x'
x = the Opera version. For example: libffmpeg.so.32
Note! Each time you update Opera to a new major version, you have to make a new symlink where you change the last number to the right one.
Then restart Opera.