Try searching in your package manager, or install/uninstall programs, for the lxde meta package. It might have a name like "task-lxde". Install this.
When prompted, choose lxsession lite. lxsession is deprecated.
This works on Mandriva (GNOME) and Ubuntu (GNOME) - most other systems are 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.
This should be all you need - if there is anything missing here, please add it.
More detailed instructions
For more details, see the page for your distribution.