Step 1: Tools and Materials
Notebook Computer - found a nice IBM Thinkpad online for $60 with a dead battery.
12V car adapter specific to your notebook - About $10 online.
12V battery - I had an old battery from my garden tractor.
12V battery tender/trickle charger - Already had this but these are $15-30 online.
12V power outlet or cigarette lighter.
Plastic box large enough for your battery, cables and at least a few inches taller. I used a plastic marine battery box, about $6 from W--mart. These are used in boats and RVs so batteries can be moved around. Plastic toolboxes, 5 gallon bucket, anything plastic and large enough can work.
Wire, terminals, electrical solder, battery post clamps (I used hose clamps), cable ties.
Step 2: Build the Cables
Find terminals that fit the blades on your power outlet and solder them to about 12" lengths of 10ga stranded copper wire. I had two different terminals, but they did both connect OK. Red and black will help keep things in order but I only had black. The other end of each wire get a battery terminal, alligator clip, or just strip about 3/4 inch of insulation and leave it for now. I cable tied the two wires in a couple of places to help keep them from tangling.
Plug the terminals onto the blades on the power outlet and fasten the opposite ends to the battery terminals. Positive battery terminal connect to the center of the outlet, negative connects to the outside coller. With the multimeter, test the polarity. Set the multimeter to DC Voltage. Place the positive (red) probe to the center terminal inside the outlet and the negative (black) probe to the outside collar. A positive reading means you've connected them correctly. If you get a negative reading, reverse the terminals on the power outlet. Mark them so they can be reconnected correctly later. You can see that my battery is low, but reading the correct polarity, so we're good to go. Also, you can see that I didn't use a battery terminal; I just clamped the bare wires to the battery posts with hose clamps. I'll fix this later. ;)
Step 3: Assembly
Now that the adapter is connected, we need to connect the charger by simply clamping the charger's red clamp to positive, black to negative terminal on the battery. This charger is small enough to fit in the box with the battery but this just doesn't seem too safe. There is plenty of room to mount the charger outside the box.
Add the lid to the box and place it low in the stand for stability. Find a suitable place for the charger. I used cable ties to fasten much of the wiring to the stand, and drilled a hold in the leg to thread the notebook adapter through the leg up to the computer.
The furniture dolly under the stand is temporary--I'll eventually mount a permanent base and casters. If you plan on making this a wheeled cart, USE CASTERS OR WHEELS WITH A BRAKE, or you may find yourself chasing your computer down the driveway!
Step 4: Summary
Depending on what you already have, this can be built inexpensively. My total cost was $75, including the notebook! I already had the shelf, charger, battery, etc. The computer and a new battery would be the highest cost items, but a battery considered useless for a tractor or car may work just fine for a notebook, so these can be found cheap. Casters could be expensive, but your local import tool store may have an inexpensive furniture dolly, or a $20 hand truck that could be adapted.
Works great for me; let me know if you've done something similar. Thanks