I searched around for quite a while and just couldn't seem to find how to add custom applications to the Unity launcher (side bar) in Ubuntu. After much investigation I have found that applications that show up in the dashboard and on the Unity launcher have corresponding appname.desktop files in /usr/share/applications/.

I created one for TeamSpeak 3 on my machine. Here is what my Teamspeak3-client.desktop file looks like:

[Desktop Entry]
Version=3.0.6
Name=Teamspeak 3 Client
GenericName=Teamspeak
Exec=/home/alex/TeamSpeak3-Client-linux_amd64/ts3client_runscript.sh
Terminal=false
X-MultipleArgs=false
Type=Application
Icon=/home/alex/TeamSpeak3-Client-linux_amd64/pluginsdk/docs/client_html/images/logo.png
StartupWMClass=Teamspeak
StartupNotify=true

Obviously you would modify the version number to reflect the version you have installed. Also double-check the path for the "Exec" and "Icon" options. My installation was located in my home directory.