How does looking at the sun damage your eye?
There are several mechanisms by which looking at the Sun without suitable protection can damage your eyes.
Ultraviolet light can cause sunburn to the eye. In particular the cornea. If this happens the eye will be very painful and can cause temporary blindness.
Infrared radiation can painlessly burn the retina. This can cause permanent damage and temporary or even permanent blindness.
Very bright light can cause Solar Retinopathy where the retina's light sensitive cells get overload and emit chemicals which can damage the retina. This is often painless and can cause long term blindness.
Normally the Sun is too bright to look at it long enough to cause damage. People have suffered eye damage from reflected sunlight from water or snow.
The safest way to observe the Sun is to reflect its image onto a white surface. A device called a solarscope works on this principle.
The Sun can also be viewed directly, even through binocular, a camera lens or a telescope using special mylar film which reduces the intensity of sunlight by a factor of several million. Mylar film is used in eclipse glasses and it can be purchased in sheets from some online vendors.
One final point is that the only time it is safe to view the Sun without suitable protection is during the totality phase of a total solar eclipse. This is an amazing sight which can only be appreciated with the naked eye or through binoculars, a camera lens or a telescope. You can, and should, view without eye protection from the moment the second contact diamond disappears until the third contact diamond ring starts to appear.