IntelliJ IDEA

tl;dr

/Users/your_username_here/Library/Java/JavaVirtualMachines/

Choose File > Project Structure > Platform Settings > SDKs

You can inspect the JDKs known to IntelliJ by choosing File > Project Structure > Platform Settings > SDKs.

Notice how the location of the selected JDK is shown in the JDK home path field.

In this example, the JDK downloaded by IntelliJ was put in:

/Users/your_username_here/Library/Java/JavaVirtualMachines/

Note that this location contrasts with the location used by some of the independent JDK installers. In my experience, those tools use the root /Library path, rather than in the user’s ~/Library. That full path would be: /Library/Java/JavaVirtualMachines.

SDKMAN!

By the way, an alternative tool I prefer for finding, downloading, installing, and uninstalling JDKs (and other software kits like Gradle) is SDKMAN!. It is a command-line tool for Unix-like operating systems including macOS.

Installing JDK

To install JDK, you can refer to help.ubuntu.com/community/Java.

If you want to install openJDK,

sudo apt-get install openjdk-7-jdk 

If you want to install Oracle JDK, you can use PPA from webup8 team.

sudo add-apt-repository ppa:webupd8team/java
sudo apt-get update
sudo apt-get install oracle-java7-installer

Installing IntelliJ IDEA

[Updated Answer]

Download IntelliJ IDEA CE from www.jetbrains.com/idea/download/.

1. Extract ideaIC-XX.Y.Z.tar.gz using

   tar -zxvf ideaIC-XX.Y.Z.tar.gz
   

2. Run idea.sh in bin directory inside the extracted folder.

3. To create command-line runner, Tools > Create Command-line Launcher
4. To create a desktop entry, Tools > Create Desktop Entry

That's it. Now, you can launch IntelliJ from Ubuntu dash.

[Old Answer]

Download IntelliJ IDEA CE from www.jetbrains.com/idea/download/.

1. Extract ideaIC-XX.Y.Z.tar.gz using

   tar -zxvf ideaIC-XX.Y.Z.tar.gz
   

2. Become root.

   sudo -i
   

3. Move the extracted folder to /opt/idea

   mv ideaIC-XX.Y.Z /opt/idea
   

4. Create a desktop file and install it:

   gedit idea.desktop
   

   and copy the following to the idea.desktop file.

   [Desktop Entry]
   Name=IntelliJ IDEA 
   Type=Application
   Exec=idea.sh
   Terminal=false
   Icon=idea
   Comment=Integrated Development Environment
   NoDisplay=false
   Categories=Development;IDE;
   Name[en]=IntelliJ IDEA
   

   then execute the following command to automatically install it in the unity:

   desktop-file-install idea.desktop
   

5. Create a symlink in /usr/local/bin using

   cd /usr/local/bin
   ln -s /opt/idea/bin/idea.sh
   

6. For idea icon to be displayed in dash, idea icon can be added as

   cp /opt/idea/bin/idea.png /usr/share/pixmaps/idea.png
   

That's it. Now, you can launch IntelliJ from Ubuntu dash.