From your problem description I get that you're using the default Ubuntu graphical environment - Unity - which is performing poorly on your video card.
If the suggestion of installing fglrx doesn't work/provide the required performance, please read below.
If you don't necessarily want to run Unity, the best idea that comes to my mind is to try an alternate graphical environment - XFCE or LXDE - which is much lighter than Unity on graphical resources.
I run a (custom, built on my own) XFCE/LXDE version successfully on systems with Pentium 4 CPU, 512 MB RAM and integrated Intel 82865G graphics card. The Intel 82865G graphics card is a very old & poor performance video card. Oh, I should also mention I'm running as LiveUSB (which eats some additional RAM).
While you could install only the parts required to run a XFCE/LXDE session, I think it's easiest to install the full desktop experience for Xubuntu/Lubuntu. Please know there won't be a huge volume of data to be downloaded as most part of the system is already there, only specific packages will be downloaded.
You can get XFCE/Xubuntu or LXDE/Lubuntu easily by running
sudo apt-get install xubuntu-desktop or
sudo apt-get install lubuntu-desktop in a terminal (CTRL+ALT+T).
After that, logout and login back in, and remember to change the session from Ubuntu to Xubuntu/Lubuntu at the login screen.
Good luck and let us know if this works!