It's not for the faint of heart, and I can't possibly get into every bit of detail, but I'll try to link all the resources you will need.
For a summarized version, make sure to check out the corresponding post on my website.
It all starts on DIY projector forums, such as Lumenlab (which is now only accessible via the Wayback Machine), DIYaudio, or if you understand French, Allinbox. The folks on these forums pioneered the idea of reusing an LCD screen into a high quality, affordable, videoprojector, by using a very bright lamp as light source and finding the proper optics to make the magic happen !
There are already a few instructables (here, here, and here) based on these designs, and other external resources (here, here and here), so I'm not going to spend too much time on the technical aspects of building a regular 2D DIY projector. Some companies are even selling kits based on those ideas.
A DIY projector is a challenge in itself, but if you're really motivated, you can go one step beyond, and make it 3D !
A first idea is to use two projectors, commercial or DIY ones, place some polarizing filters in front of their objectives, and align the images on the screen so that they overlap. This has also been proposed in previous instructables, in some forums and other blogs.
However if you have only one LCD screen, you can still pull it off, with a little trick.