The Box. Our box was designed based on approximate specification on Chris Johnson's web site (Austin's first Screech Owl Cam). Here is a Photo of Chris's box, which is very similar to ours. Our box has a lexan partition between the owl living quarters and the camera compartment. The owls would dislodge, dirty, (or even in their curiosity, destroy) camera equipment they had direct access to. We had a friend build it for us as a surprise gift!!
A less labor intensive (but not as satisfying) alternative is to buy a ready-made owl box and just mount a camera below and facing the outside of a box. However, as nothing exterior happens during the day, it's not as exciting. The real fun is inside! An outside camera must be mounted far enough below the box to avoid interfering with the owls' flights. At least 3-4 feet.

The camera. My camera is a PC88WR ($115) from Supercircuits.com (a video security store in Liberty Hill).
With it I bought a Wide angle 2.5mm lens: Part# ML2_5MM ($30)

Lighting. An owlcam needs some amount of infrared lighting, even during daytime. The easiest is the 20 LED IR illuminator (Part # IR20, $50). If you have a glass or lexan partition you do not want a camera with built-in illuminators, as these are mounted too close to the lens and will cause reflection.

Cabling. You will need to get power to the camera and IR Illuminator, and get video (and maybe sound) back from the box. You can buy extra equipment to get wireless video transmitters, but short of solar, there is no wireless power, so you need a cable anyway. There are all-in-one video-audio-power cables, which is what I use. You'll have to figure out how to get the cable to your computer from the outside (drill a wall, or through a window). If it's a pain to run a cable directly from your computer, you could combine an outside power plug with wireless video transmission.

Video Capture card: You need a video capture card for your computer to receive the video signal. Any capture card will work. I use one by Hauppauge (WinTV Go). Most of the cheap ones will work. Probably about $25-50.

Webcam software If you want to share your camera with the world, you will need some software to take the video feed and serve it up. If you only have a few visitors, you can do this from your home PC. Alternatively, there are several programs available that will capture frames every so often and upload them to a web server. To go this route, you will also need a web server. I use webcamxp. There are others. You'll need the following features:
- ability to rotate the image 90 degrees (videocameras are horizontal, but owlboxes are vertical)
- ability to either be a webserver (if you're using your home computer as the server) or upload photos (usually by http or ftp) to a webserver.
- I also enjoy the software motion detection feature, which will capture frames any time there is movement.

Supercircuits is very helpful on the phone, (800)335-9777, or (for those in the Austin, Texas area) in person.
So, parts from Supercircuits were:
CON-6 - BNC Male to RCA Male
DC12-500R - 12V DC 500 mA Regulated Power Supply
EXT100 - 100' Video Audio Power Cable
IR20 - Compact IR Illuminator
ML2_5MM - 2.5mm Micro Lens
PC88WR - High Resolution B/W Weatherproof Camera
YPOWER - Y Power adaptor (to split the power to the camera and the IR Illuminator)