I found the solution to installing Quartus II Web Edition v10.0 on this website:
http://fpga4u.epfl.ch/wiki/Install_Q...he_Installer_2

Basically the installer has a conflict with libX11.so.6, however there is a simple workaround.

  1. Start the installation process with "--confirm" to pause before each step
    Code:
    sh altera_installer.external.sh --confirm
Creating directory bin
Verifying archive integrity... All good.
About to extract 49568 KB in bin ... Proceed ? [Y/n] Y
Uncompressing Altera Installer............................................................................................................................
OK to execute: ./altera_installer_gui --gui  ? [Y/n]
  2. Delete libX11.so.6 to remove the conflict
    Code:
    cd 10.0sp1_quartus_free_linux/altera_installer/bin
rm libX11.so.6
  3. Continue installation process. The GUI installer should now appear.
    Code:
    OK to execute: ./altera_installer_gui --gui  ? [Y/n] Y
Fontconfig error: "conf.d", line 1: no element found
Fontconfig warning: line 73: unknown element "cachedir"
Fontconfig warning: line 74: unknown element "cachedir"