Actually,Ubuntu 's default ATI driver can enable some Compiz effects already,but the default driver's effect is not good,so we use below ways:

Method 1:

We may install open source ATI video card driver : System->Administration->Hardware Drivers,tick the driver you need ,and then click it to intall.

Method 2:

Intall ATI official driver,below is the download link :

AMD displayer driver 8.42.3 is availabel .AMD added AIGLX surppot for linux user permanently since this version,it means that we can easily run Compiz Fusion or Beryl with ATI video cards from now on.I think all linux fans who use AMD display card will be happy to hear that,although it is too late for supporting AIGLX.