Mandriva

This is for 2009 edition.

Go to Mandriva Control Center

- Install Software

- search lxde and choose the meta-package, task-lxde.

When prompted, choose lxsession lite. lxsession is deprecated.

That's it!

Or you can use the console on root: urpmi task-lxde

Running LXDE

This works on Mandriva (GNOME) - starting from other desktops is probably similar.

From the menu, select:

System -> Administration -> Login window

This will give you a dialogue box:

You may want to uncheck "Default session" so it gives you a choice at login (not sure if this works). When trying a new desktop environment this makes sense, so if there are major problems, it's easy to use a different one next time. Once you have settled on a new choice, you may wish to set this as default.
Under "Security" if you uncheck "Automatic login" it will give you a dialog box to enter your password at startup. (This gives you time to make your choice.) Then, at startup, look for the session options. This might be a symbol like a paper and pen, displayed under the password box and next to the shutdown symbol. Choose LXDE, and start up.