One way of observing the Sun is by looking at it through a welding filter in order to avoid injury due to IR and UV radiation. Retinal burns are also possible with prolonged exposure to direct sunlight. The image below was captured with the filter between the Sun and my Kodak Z981 camera's zoom lens and a manual exposure setting (ISO Speed: 100, F-Stop: 8.0 and Shutter Speed: 1/800 sec). I also used the manual focus setting which helped to stablize the camera. To keep the filter in place in front of the camera I taped it to a tube of paper that slipped over the zoom lens. The Eye LCD viewer made it easy to change the settings in daylight since the screen at the back of the camera was totally unusable.
I got the welding lens several years ago at a local hardware store. It appears to be a polycarbonate filter and with a "10" stamped on it (Shade 10?). The filter blocked practically all of the blue portion of the image above and reduced the intensity of the Sun's light considerably.
The Sun is not a perfect Lambert radiator but exhibits limb darkening. The plot below was obtained from the image of the Sun by computing rounded values of the pixel distance, r, from the center of the Sun and then averaging over those pixels with the same distance. The plot was rescaled so that the peak value is 1. Note also that the vertical scale is nonlinear due the picture's encoding format.
It is difficult to accurately determine the angular size of the Sun because of the Sun's corona which is just noticable in the plot. There also appears to be evidence of a solar atmosphere. Some of the extraneous light might be due to scattering off the Earth's atmosphere or in the filter. With maximum zoom one gets an image of the Sun that is about 800 wide for 14 megapixel images. The resolution of the image is limited by the aperature of the camera's lens. It appears that this method will work for simple images of the eclipse a few months from now.
Supplemental (Feb 25): GONG Sun images