Light painting is a tecnique to control lighting in photography. Also flash photography is a simple light painting, because you choose where flash is pointing, how much powerful it is, which colour its light is. But this tecnique could be very complicate too, as you can see with a simple Flickr search.
My contribution at this nice modern art has been done in different ways, with a neon light, with a led stripe, and even with car's headlights ;-)
Now I explain you how to build a neon paintbrush.

Step 1: One Option

To recover a neon portable light you have different choices. You can search a little desk usb lamp as this one, which has already a nice container, a good switch and needs a power of only 5 volts. With this you only have to cut the USB cable and connect it to a battery holder. Or you also could retrieve a female USB socket to keep intact the desk lamp. You certainly don't need an instructable to build this type of neon paintbrush ;-)

Step 2: Another Option

But maybe you already have a neon light taken from an old PC case. These lights are longer than the desk lamp, but they usually haven't an holder, and they work at 12 volts. So it's a little more complicate transform them to our purpose.
Here is the narrow neon tube already extracted from his plastic cover. This neon tube has both cables come out from one extremity, but if you look closely you see a very thin metal wire which runs side by side the tube.

Step 3: The Mirror

Here you see what we need to hack it into our brush. The blue box is the transformer circuit which is usually connected to the neon light. It's not exactly the same I've used, but they do the same thing. If you have the original circuit of your neon tube you should better use that. The thing over the box is a narrow mirror, you could retrieve one as this from an old scanner. If you don't find a mirror you could use a metal profile, a plastic pipe, or something similar, better white or reflective.

Step 4: The Circuit

Here is how I connected my circuit on the battery holder. I can insert 8 AA batteries here, for a total of 12 volt, as required. My neon tube has two wires comes out from both the extremities, and I've decided to hide them behind the mirror. The mirror (or profile, or pipe) also attends to support the glass pipe, which is very breakable.

Step 5: Add a Pushbutton

You can see here that I've had to add a switch and a pushbutton to the circuit. you'll not find them on these types of circuits because in PC case you don't need them. Simply solder then in series with one pole of the batteries. Pushbutton is useful when you want to type a word in the air, and so you need to turn on and off the light very fast between a character and the following. The circuit has an high voltage section to start the neon tube, pay attention at not touch it when circuit is powered, and tape it when everything is assembled.

Step 6: Add an Hook

Then also an hook is very useful to hang the light to a rope and make it swing, as I've done in my pictures. I've bent a steel wire, and I've glued it into an hole. If your battery holder has a different shape try to find the balance center, so that it will stay well hanged.

Step 7: Glue Everything Together

I've used two elements glue to attach only the extremities of the neon tube, so that nothing "compromise" the reflection in the full lenght of the mirror. Then with that powerful glue I've also connected the center of the mirror with the flat side of the battery holder. This forms an handy shape wich is very convenient to keep the tool in the hand and act with the thumb on the pushbutton.

Step 8: Hang It Up!

Then I've used contact glue to keep the wire in place behind the mirror. Try not to use cyanoacrylate glues, because it's difficult clean the mirror if you by mistake glue the surface. You can see the "brush" tied to a rope. Now you only have to lie your camera on the floor, turn off the lights, and find the right distance and exposure time. These parameters could vary depending on your lens length and on the type of drawing you've in mind.

Step 9: And Shoot It!

These are some nice effects I've obtained let the light swing and swirl forwards and backwards, in an exposure time of about 4 seconds. I've used a 18mm lens at about 1 meter from the hanging (to ceiling fan) light. You could adjust colours in Lightroom or Photoshop.
Don't forget to try different tecniques, typing in the air, throw the neon (better on a sofa), move it as sea waves, bandage it with some coloured flash filters... and let us know if you think up something original!