It is important to remember that it is very, very dangerous to look at the sun with the naked eye. This applies as much during a partial eclipse as it does during full daylight. It also includes observing it through a telescope, binoculars or a camera view-finder. To do so is to risk damage to the eye or blindness.
It is however safe to observe a total eclipse, even through magnification, but it is important to keep an eye on the clock and be ready for the end of totality.
Filters are available for viewing the sun through, however. But make sure that any that you buy have the CE mark which ensures their safety standards.
It is also possible to view the process of an eclipse using a pinhole camera effect , using this to project an image of the event onto a suitable surface. This effect can also be found occurring naturally, try looking under a tree for gaps in leaves causing circular pools of light. Such gaps can act as pinholes, projecting the eclipse onto the ground.
It is possible to photograph or video a total eclipse, although during the partial phase appropriate filters should be used, as with viewing the phenomenon with the naked eye. A long focal length lens is recommended for a reasonable sized view of the eclipse itself – somewhere around 2000mm for a stills camera and 300mm for a video camera.