Just as the title suggests, two ways to use Teamviewer remote support software on Ubuntu client PCs.
Install Teamviewer on default installation (requires root / sudo access!):
sudo wget http://download.teamviewer.com/download/teamviewer_i386.deb && sudo dpkg -i teamviewer_i386.deb || sudo apt-get -y -f install
sudo wget downloads the software (sudo is not really necessary here actually), sudo dpkg then tries to install it using the debian package management which will fail due to missing dependencies and thus cause apt-get to repair the Teamviewer installation (by downloading all necessary packages).
Start Teamviewer on Ubuntu client PC without installation (no root required!)
wget http://download.teamviewer.com/download/teamviewer_i386.tar.xz && tar xvfJ teamviewer_i386.tar.xz && ./teamviewer/teamviewer
wget downloads the software, tar unpacks it and the last element starts the software
Hope this helps,