Many thanks to Doppler12 having this guide that I graciously lifted in order to update :D
Due to the Dolphin Dev Teams Linux Package Maker being newer than latest LTS we will have to continue to build our own Dolphin. You will have to uninstall/remove current dolphin-master build you're using for the time being. You can reinstall it later. This build will show up as #### as I merged a pull request that auto includes the udev rule exceptions so the Wii U adapter works by default (report-ably excludes some builds of Arch).
If you have Ubuntu Ver: 15.04 or later: Click Here and follow through with the basic installation/builder.
If you use arch and are comfortable with PKGBUILD's then Nicman23 has written one for use. PKGBUILD
First you will need to obtain the dependencies for compiling dolphin. Even if you've built a previous version of dolphin, there are new dependencies
You will need to check your GNU compiler version, with the terminal command
It needs to be at least 4.9.1, if it is not you will need to update it. For Ubuntu 14.04 and Mint 17 follow this GUIDE
Now once the legwork is completed you will need to follow these steps in terminal:
git clone https://github.com/dolphin-emu/dolphin.git
git checkout ce493b897d6d3735c930a8465cc0c26bbe5feb86
make -j5 (The number after j is cpu core count + 1)
sudo make install (Will not work if you do not install, you can change its name later)
Now to rename our newly built and installed dolphin. (If you use no other versions of dolphin, don't bother with these steps)
sudo cp /usr/local/bin/dolphin-emu /usr/bin/dolphin-nand
sudo rm /usr/local/bin/dolphin-emu
sudo rm /usr/local/bin/dolphin-emu-nogui
sudo cp /usr/local/share/applications/dolphin-emu.desktop /usr/local/share/applications/dolphin-7480.desktop
sudo gedit /usr/local/share/applications/dolphin-7480.desktop (then edit the name to whatever you want and change the exec to dolphin-7480, change the icon too if you're so inclined)
sudo rm /usr/local/share/applications/dolphin-emu.desktop
And now you should have a menu option for Dolphin-7480 and be able to install whatever other copy of dolphin master you'd like to be using.
Launching games fails with "WriteRest Op" error
Add "-fno-pie" to "CXX_FLAGS" when building Dolphin.
Launching Wii games in Netplay fails with "Invalid SYSCONF" error
This is why I told you to sudo make install
Thanks to Nicman23 for pointing out a new issue with compiling dolphin and finding the solution. Certain versions of miniupnp cause dolphin to fail to compile properly. Compiling now requires to use DUSE_UPNP='FALSE' flag.