One nice little app I've used to create Launchers for my desktop is Arronax.
http://www.florian-diesch.de/software/arronax/
But a quick google search for "teamspeak" and "ubuntu" gave multiple hits about how to install. The following link also brings up a good question is "either" your ubuntu -or- the teamspeak you downloaded 32Bit instead of 64Bit?
If your ubuntu is 64 bit but the app is only 32 bit then you need to install the 32-bit compatibility libraries, you should be able to run 32 bit programs normally by adding:
sudo apt-get install ia32-libs
The folloiwing post also had good info for teamspeak setup:
How to install Teamspeak 3 client on ubuntu 12.04 lts 32 bit?
it states:
1) cd ~/Downloads (assuming saved in Downloads folder, otherwise where you saved it)
2) chmod u+x ./TeamSpeak3-Client-linux_x86-3.0.12.run
OR if 64bit version:
chmod u+x ./TeamSpeak3-Client-linux_amd64-3.0.13.1.run
./TeamSpeak3-Client-linux_x86-3.0.12.run
OR if 64bit version:
./TeamSpeak3-Client-linux_amd64-3.0.13.1.run
3) Press enter to view the user agreement
4) Press Q to leave the user agreement
5) Type Yes to create the folder (named TeamSpeak3-Client-linux_xxxxxx)
6) Open the folder, Run program called ts3client_linux_x86 or ts3client_linux_amd64