Try using LXDE. It is lighter than Unity (the default DE) and will speed up your computer.
For 12.04 and later versions, you'll need to do this through a terminal.
Open up a terminal (Super, then type Terminal
into the dash), then run the following:
sudo apt-get update && sudo apt-get install lubuntu-desktop
Or install via the Software Center:

You will get asked to enter your password, and you will also be asked to choose between LightDM
and LXDM
- I suggest using LightDM
.
Once that is done, log out, and then select Lubuntu
as your desktop session:
