Windows server 2008 R2 or later, Server 2008 (i.e. the Vista based Server OS is no longer supported.)
Install the TeamSpeak Server
Download the latest version from your preferred vendor, at the time of writing WinRAR is at version 5.50, so we will download WinRAR x64 (64 bit) 5.50 from http://www.rarlab.com/download.htm
Download the latest TeamSpeak Server for Windows from http://www.teamspeak.com/en/downloads.html#server at the time of writing this is Server 64-bit 18.104.22.168
Extract the archive to anywhere you like on your system, ideally you do not want to extract the files to any of C:\, C:\Windows\, C:Program Files\, as these folders are protected by windows UAC and may be problematic later.
Browse to the folder you extracted the files in and run ts3server.exe.
A window will pop up with information about your server, save this information in a safe place as you need it to become server admin.
With your TeamSpeak client connect to the IP of your server, when you connect a windows will pop up asking for the server token, this is the longest random string you were given in the previous step, enter this and you will be given server admin.
You can now administrate your TS3 server instance as you like.
Now you have your shiny new server, why not promote it on a TeamSpeak Server List? The extra exposure could help you become the number one server on the planet some day.
All of this too much? You can make a free Private TeamSpeak channel on many public servers.