Anyways, I thought I'd collect what I learned and publish it so that people can go ahead and make even cooler screen+painting combos.
Step 1: Get the stuff
The picture is missing quite a few pieces, but you probably know what they look like anyway.
Step 2: Make the inner frame
Step 3: Clothing it
The tensing process is a lot of work since the fabric need to be stretched really hard in order to avoid ugly bubbling effects. You start out by spreading the fabric centered onto the frame, folding it over the back and putting one staple at the middle of each side on the outside of the frame. Don't put the staples too far "down" or you'll have problems when stripping off the excess fabric when done. The first ones are the most tricky and you might have to pull them out and tighten several times before it looks okay. It's not crucial that it looks great at this stage. You can proceed by putting three or four staples around each initial staple and tighten it until you're satisfied. Always alternate between sides to minimize the risk of pulling the fabric askew since it leads to bubbling.
Step 4: Streeeetch
Then it's time to do the other side. Take care not to get the side that's done dirty in the process since it will be problematic to clean it. The material I used for this is called Barracuda which is a plastic tarp similar to the stuff they use for printing advertising banners on. It's kindof thick, a couple of millimeters at least, so it's much harder to stretch than the shades and you should probably get a mate to help you out. Aside from that the process is pretty much the same. Remember to start out by stripping the excess fabric left from the other side using sharp scissors though (box cutters are too imprecise for a good result).
Step 5: Bring in the Gimp
So with that we turn to Gimp (I'm sure a number of other applications will do just as well, but the examples will be in Gimp). First off we convert the image into greyscale (Image->Mode->Greyscale), then we erase the details we aren't interested in, this makes the following step somewhat easier. The next step is the Threshold tool (Tools->Color tools->Threshold) where you can fiddle with the detail level until you're satisfied.
Before moving to the next step we need to make sure that the white parts of the image are transparent rather than white (they probably aren't). Easiest is to go back to RGB, add a background layer and flood fill it with some other color and make sure that there is an alpha channel present (Layer->Transparency->Add Alpha Channel). Then use the wand (actually, "Fuzzy Select" is the proper name) tool and start selecting all the white parts and delete them (zoom in to get the smallest parts).
If the image is small, now is a good time to make it the intended size before applying the Oilify filter (Filters->Artistic->Oilify). Before oilifying the image will be rather "prickly" but the oilifying takes care of that and the end result looks really professional.
Step 6: Be artistic
I didn't trust my abilities to mix shades consistently so I just got the three different oranges that were available (acrylic colors) at my local paint pusher.
Step 7: Paint the whole shebang
Once you're done painting the edge you screw on the outer frame. Now, if I got to do it all over, I wouldn't have chosen to do the outer frame in two pieces. The original plan was this: the outer frame would consist of eight finished and miter jointed pieces (30mm x 17mm each) forming a two-layered frame. The first four, inner, pieces would be fastened by screws and then the outer framed would simply be glued onto the inner one, that way I couldn't have to cover up ugly screw heads. This was a bad idea because of the miter joints. Since I kindof skimped on the miter box, the precision wasn't really up to par, but even if it had been, it would have been almost impossible to get all the sixteen (yeah, that's right) angles to align properly. You also need to screw in the loops from which to hang the whole thing.
Oh well, time to paint. I hung the screen and fed the image to the projector. The first thing you should do is to put masking tape along all straight lines since it's harder than it seems to paint along a straight line. I thought I could get away with it but had to go back and redo the lines afterwards. Be sure to seal the edges of the tape as seen in the pictures so that the paint doesn't bleed in under the edges of the tape.
After the lines are done, the rest is just hard work. I figured it would take a couple of hours, but it ended up with me going to bed at five in the morning (I'd started painting at about eleven I think, it's all a haze actually). Since I had my flatwarming party the next day I really wanted it to be ready by then.
Step 8: Lessons learned
Anyways, the joints on the inner frame and the outer one are really the only two thing I would have made different if I did it again. Now go forth and make even nicer paintings!