You will need the latest version of the SOE Matrix Online client already installed on your system
If you do not already have it, download it from this link: MatrixOnline.7z and extract into a directory of your choice using 7-Zip or WinRAR
It is recommended to use a download manager to download this file, as it is quite large (1.6GB). The one i recommend is Free Download Manager (freedownloadmanager.org).
After you have the Matrix Online client installed, download the MxoEmu TestServer Launcher installer from here: MxoEmuTestServer.msi and run it.
During the installation, your antivirus might detect the file MxoEmuTestLaunch.exe as a virus. This is because it was packed to reduce the size by more than half. Add the file or folder to your AV's whitelist.
If you have UAC on, and The Matrix Online is installed in a priviledged directory (such as Program Files), you will have to set the launcher to run as administrator so it can access the files it needs.
When you first start the MxoEmu Test Server Launcher, it will ask you to find the directory in which you have The Matrix Online installed. After that, it will not ask you for it again. With the launcher open, simply click the Launch button to start the configured instance of The Matrix Online, and login as normal.
In-game character creation does not work, so use this website to create them and customize their appearance and location.