This guide is out of date. Use https://github.com/FAForever/faf-linux instead.
Install PlayOnLinux with your package manager (i.e. sudo apt-get install playonlinux). Then, type playonlinux and wait for it to refresh its list.
Install Steam under PlayOnLinux. Once Steam is running, exit it, select its entry in PlayOnLinux, and select Configure.
I suggest using Wine 1.7.8-d3d doublebuffer
Now go to the "Install Components" section and install, in any order: d3dx9, directx9, dotnet40