The important thing to remember is never look directly at a partial eclipse without proper eye protection. Permanent eye damage can result. It is best to use a pinhole camera or other method to project the image of the sun onto a surface to look at. To look at an eclipse directly, use only number 14 welder's glass, a mylar filter, or a metal-on-glass filter bought from a welding supply shop or astronomical outlet. Do NOT use exposed film, sunglasses, smoked glass, polarizing filters, or photographic neutral density filters. These will not filter out infrared radiation, which can damage your eyes in a very short time. Telescope "sun filters" which screw into the eyepiece should also be avoided, as they can overheat and crack when sunlight is coming through them, and retinal damage can occur instantly. See below for more details.
NASA's Eclipse Page
Total Solar Eclipse of 1999 August 11 - NASA Eclipse Bulletin
Tips on Eye Safety during an eclipse - School of Optometry, University of Waterloo