Double click on the icon that was put on your desktop to run the TeamSpeak 3 program. It should look like the picture below.
Open the Connect Window
At the top of the TeamSpeak 3 program you'll click on the "Connections" menu then click the option named "Connect".
Enter Connection Information
Enter in the hostname such as useast.teamspeak3.com for the "Server Address" section. Lastly you'll need to enter in a "Nickname" for you to connect as, this is the name that will people will see you as.
If you've successfully connected to the server it should look similar to the picture below.