Before you can install any Linux Distribution on Windows 10 you will need to install the Windows Subsystem for Linux Feature.
There are two way to install this:
1. Open a Powershell as administrator and run the following command:

PowerShell
Enable-WindowsOptionalFeature -Online -FeatureName Microsoft-Windows-Subsystem-Linux

2. Or you can install it in the Windows Features
Control Panel – Programs and Features – Turn Features on or off

Installing Fedora on Windows 10

Since there is no Fedora subsystem for Windows yet, I had to purchase Fedora Remix for WSL from the Windows Store. This only set me back $5. The installation process was point and click.
Open the Microsoft Store, search for Fedora, purchase Fedora remix and install

Fedora Remix

Note: There seems to be a slight issue with the clear command.
Update your packages:

Running Linux Desktop Apps

Most terminal apps seem to install fine but if you want Linux desktop apps you will need to install an X Window Server. I used X410 which sets you back $10 in the Microsoft Store.
Open the Microsoft Store and search for X410, then purchase and install.

Now that X410 is installed, lets install a Linux GUI application and test it out.
I am installing gedit.
# sudo yum install gedit

Install gedit
# sudo yum install gedit

Run gedit
# gedit