I've had this idea for a while, and it's gone through several incarnations in my head as I've tried to piece it together. It's still currently a work in progress, but I decided to at least show what I have so far. Maybe you folks can offer some additional ideas for Version 2.

Otherwise, enjoy, and feel free to copy this idea!

I tried to find a still of it for illustration, but I couldn't find one. If you watched Futurama, however, you'll recognize it. It usually shows up behind the couch at Fry's apartment.

Step 1: Gather Materials

This step is exactly what is listed in the title. Gather things for the making of this project. Here's a brief rundown of what I used and approximate pricing.

Materials
4x6 curved picture frame - preferably black (otherwise can be spray painted) -$7
Black Spraypaint - $5 (if necessary)
Aluminum foil - $.97
LED Hanger Lamp - $6
Acrylic Paint in black along with bright blue, green, and pink - $3 apiece
Adhesive - I used DulcoCement, since I had it from a previous project
Spackle - already had some
Clear tape
A few thin paintbrushes
Some velcro strips
Lots of patience

and...
the Following Logo Pattern

Step 2: Preparing the Image

1. Remove the glass plate from the picture frame.
2. Tape the printed-out-logo to the side of the glass that you want the image to appear on facing inward.
3. Use the logo as a tracing tool to hand-paint the logo onto the paint. I painted the black outline of the logo first, followed by the green slime, blue background, then pink lettering.
4. Remove the taped-on-logo.

Tip: I suppose the order is really up to you, depending on preference. However, be sure to perform each step separately, so as to not allow the paint colors to mix. Also, paint over each layer a few times, just make sure it's thick enough so that you don't see what's going to be behind it. However, don't paint so much that no light can go through.

Step 3: Preparing the Frame

1. Remove the hangers from the back of the frame. Fill the screw holes with some drywall spackle or wood putty, depending on what's available to you. Allow to dry. Use some sandpaper to smooth it out if necessary.
2. Spraypaint the frame black, using thin even layers. Don't worry about painting the side of the frame you plan to face away from the front unless you just really want to be consistent with your work.
3. Glue the painted glass into the frame so that it will face out correctly, with the paint inside.
4. If you want to make the final product brighter, you may glue some aluminum foil around the inside of the frame to reflect more light toward the window.

Step 4: Preparing the Backing

1. Carefully take apart the LED lamp and place the LEDs in the middle of the backing. Glue down. Be careful so as not to remove the current soldering! I made this mistake and had to do some rewiring.
2. Glue the switch and battery case down as conveniently as possible, making sure it will stay behind the frame once attached.
3. Glue strips of aluminum foil on the backing around the lighting device so as to create maximum light output, if you so choose.
4. Attach Velcro strips to the back of the frame and to the edges of the backing. Top and bottom were sufficient to stick it together.

Thoughts: If I were to do this again, I would probably cut a hole in the backing so that the switch and/or battery would be placed on the reverse of the backing. This would remove the need for the Velcro strips, as I could have just glued it shut completely.

Step 5: Final Step and Ideas

Assemble and enjoy!

Additional Thoughts for Version 2

The original lamp used a pull-chain. If I could modify this to use one, it might be a little more "canonical." Also, I could have gotten a plastic decal printed out, probably at the local copy store, to stick to the glass, to make the image a little more clear. However, I almost prefer the hand-painted look this creates. It may also have been good to have more light dispersal within the lamp. I considered using a small fluorescent tube light, but apparently most 6 inch fluorescent tubes operate within a device that's slightly longer the 6 inches. I'm also considering trying to find some black weather stripping around the image to clean it up a little bit.

Good luck with your own projects, and feel free to comment, advise, or try it yourself!