My fiancée is very keen on arts and crafts. A light box was just what she needed to be able to trace patterns onto paper and cloth.
This light box is cheap, safe and easy to build - I put it together in two hours.

A key part of this design is maximum insulation between the internal components and the outside. This is essential with any design that involves mains electricity.
As a consequence, all solder joints are located within the box, there are no metallic parts that protrude from the inside to the outside of the box, and the electrical cord was held in place with a cord grommet to prevent the cord being cut by back and forward motion.

Step 1: Materials and Equipment.

The light box was built from the following materials:
A cheap student lamp ($10 AUD).
A strong, thick-walled plastic container with a transparent flat lid that clips in place. ($12).
An electronic cord grommet. (You can buy a pack of 10 for $4).
An energy-efficient light bulb. ($4 or $5, depending on where you brought it.)
Two-part araldite glue. (A bit under $2 for one pack)
A piece of waste polypropylene (Aka. part of a cheap cutting board I bought years ago in a dollar shop.)
Hot glue.
Shrink wrap.

Extra equipment included:
A drill.
A nibbler.
A wire stripper.
A hot glue gun.
A solder gun.
A hot air gun

Step 2: Disassemble the Lamp.

The one picture I didn't take was of the lamp before I got all Freddy Kruger on it.

Basically the steps are:
1) Unscrew the base and cut the wires connecting the switch to the light socket and the power cord. Make sure that you leave 3 cm of wire attached to the switch - this will make it easier to resolder once everything is installed.

2) Use a screwdriver or bread knife to pop the switch out of the base. (It had two little tabs on the side that had to be pushed in. Once this was done, the switch just slid out of the metal base.)

3) Pull the power cord free.

4) Disassemble the light head. This involved removing two small metric fasteners, loosening a restraining nut, and yanking the light socket and cord out of the reflector and flexible head. Keep the metric fasteners , we will use them later. You might just be able to make them out attached to the light socket. I did this to ensure I didn't misplace them.

You will end up with a power cord, a switch, and a light socket, all with cord attached to the terminals.
You will also be left with a few odds and ends that you may be able to make some use of in other projects. I was surprised to find that the base was weighted down with a big block of wood.

I guess that's what you get when you buy a budget lamp.

Step 3: Attaching the Light Switch.

Now we can get to the building steps.

5) Using a drill, drill a pilot hole in the middle of a short side on the container.
(Note my little drill press? These things are awesome - I was able to pick this up for $40.)

6) Use the switch to measure out the appropriate size hole to cut into the container. It's important that the hole be as tight as possible, as the little tabs on the switch will lock it firmly into place once installed and prevent it slipping loose. It's always possible to enlarge the hole later if you undercut things.

7) Using a nibbling tool, expand and shape the hole to a rectangle.

8) Once the hole is cut to size, push the switch through. I set it up so that if the switch was knocked by a downwards strike (As if something was dropped on it), the lamp would turn off.

Step 4: Insert the Power Cord.

9) Using the drill, drill another hole in the same side of the container.

10) Strip the outer insulation off 5 cm of the cord, then strip the inner insulation off both inner wires.

11) Attach the grommet to the cord, with the rounded edge facing outwards towards the plug.

12) Push the cord and grommet through the hole. The grommet will click into place.

Note: Whenever dealing with a cord going through the side of a case, you should ALWAYS use a cord grommet. It will hold the cord tightly in place AND prevent the edges of the hole cutting through the insulation.

Step 5: Mounting the Light Socket.

The light socket was mounted like this to prevent any metallic bolts or fasteners from protruding from the box.

13) The light socket was used to measure two holes through the polypropylene block that line up to the holes on the light socket.

14) Use the drill to put two holes through the polypropylene. Make sure that the drill hole is just wide enough that the metric fasteners are easy to screw through, but not so lose that they fall out.
I had to countersink the bottom sides of the holes to make sure the fasteners fit through the plastic.

15) Use the metric fasteners to attach the socket to the polypropylene block as shown in the second picture.

16) I originally used two-part araldite glue to attach the plastic block to the bottom of the container, but it popped off in the first day of use. Hot glue will hold the block down with a flexible connection that won't pop loose so easily under stress. It's been in use for several months, and hasn't come loose yet. In the third picture, you can see that I placed the socket at the other end of the box. This is to prevent any potential shorts on the switch or cord coming into contact with the metal of the socket. Make sure that you measure how far the socket needs to be away to give enough clearance to the light bulb, not just when in place, but also to screw in and out of the socket.

Step 6: Solder and Shrink Wrap.

Now all we have to do is reconnect the socket, switch and power cord.

17) It's important to slip the shrink wrap onto one of the wires before you solder. It's also important to move it far enough up the wire, that the heat from the soldering iron won't cause it to shrink prematurely.

18) Connect one of the power cord wires to one end of the switch, and the other cord to the light socket and solder in place. We're dealing with AC power here, so the order doesn't really matter, but it is a good idea to get the colours of the power cord to match up with the colours of the light socket.

19) Connect the remaining wire of the socket to the other end of the switch and solder.

20) Slide the shrink wrap over the joins and shrink in place with a source of hot air. I use a butane pen torch with a hot-air attachment, but apparently a hair drier on high works just as well.

Step 7: Screw in the Lightbulb - Complete.

21) Screw in the energy-efficient light bulb and clip on the lid of the container. The light box is now ready to use.

I used this type of bulb for several reasons.
Firstly, the original student lamp had a wattage rating of only 20W. Putting in a light bulb that exceeds this, risks the wires, switch and connections overheating and causing fire or an electrical shock.
Secondly, energy-efficient bulbs run cooler and last longer, making this much more comfortable for my fiancée to use in her lap.