I am afraid you'll have to open the command line of your first day of Linux (don't worry, happened to me too). Applications -> Accessories -> Terminal. Type
lspci and hit Enter. This lists everything connected over PCI or PCI express, including the video card. Read through the list until you have seen something about ATI or nVidia or one of Intel's models.
Then go to Wikipedia's comparison tables for video cards to find out the OpenGL version your card supports.
Intel Graphic cards
nVidia graphic cards - here you have to click to the page for the correct generation, e. g. GeForce 7 series if you have a GeForce 7600 GS
ATI grapchic cards
Remember that these only say which version the hardware supports. To be able to run OpenGL libraries, you also need a driver which supports them. There are multiple video drivers for each chip generation for Linux. Ubuntu comes with open source versions, which are not bad, but generally a step behind the proprietary drivers released by the graphic card manufacturers (which are often referred to as
binary drivers or
proprietary drivers). If your check turns up that your hardware supports OpenGL 2.0 (which most do), you can try the proprietary drivers. They are called nvidia-current for nvidia and fglrx for ATI. For Intel, there are only open source drivers.