On 20th May 1966 a partial solar eclipse was visible from where I then lived in southern England. I was aged 13 at the time, and my school class turned up for a science lesson to find the teacher hard at work "sooting" glass plates and vessels on a Bunsen burner. Each armed with a suitably darkened piece of glass, we trooped outside to witness the eclipse by looking through the pieces of glass. There is no way that a teacher would be allowed to do that today!
At that time, the general advice for a shield for the eyes when watching eclipses was to use black-and-white photographic negatives, preferably several of them on top of each other, bearing in mind that there are lighter and darker patches on a negative. However, this advice was unsafe then, and in any case most people would find it difficult to follow today in the age of digital photography!
In any case, both the above methods could be highly dangerous, and cannot be recommended, any more than can the use of ordinary sunglasses. The point to bear in mind is that the light from the Sun is extremely strong, and looking directly at it is always a bad idea. It is possible to damage one's eyesight permanently by looking at the Sun for only a few seconds, even when it is partially obscured during an eclipse. It is worth bearing in mind that even if only one per cent of the Sun's disk is visible, the light coming from it is a thousand times brighter than that coming from a full Moon. The only safe time to look straight at the Sun is when it is an orange ball very low in the evening sky, and I have observed a partial eclipse in this way (almost certainly the eclipse of 31st July 1981).
What you must never, ever, do is look through a telescope or binoculars directly at the Sun, even if you think you have obscured the lenses in some way. Concentrated sunlight focused on to an eyeball is guaranteed to cause blindness in a very short time. Losing one eye is bad enough, but anyone foolish enough to use binoculars for this purpose may find that a flash of sunlight is the last thing they will ever see.
So why is it so bad to use eye protection such as blackened glass or very dark sunglass material? One reason is that you cannot, as an amateur, guarantee that you have sufficient protection for the intensity of sunlight in question. Another is that your protection might slip, or have cracks in it that let the sunlight through. You cannot afford to take the risk.
There are professionally produced filters you can use that have been tested and found to offer the right degree of protection. The optical density of such filters must be at least 5.0, which will reduce the intensity of the sunlight to something like 0.01%. However, you must not look at the Sun for a long time, even with such protection, and never use binoculars when wearing filter goggles, because the magnification given by the lenses will exceed the safety margin of the filter.
The only really safe way to observe a solar eclipse is to do so indirectly, by projecting an image of the event on to a light-colored surface, such as a sheet, piece of paper or card, or a blank wall. You can do this with nothing more complicated than a piece of card with a very small hole punched it in, which then acts like an old-fashioned pinhole camera. The projected image will be upside down, and will be better if you can remove as much other sunlight as possible, for example by placing the pinhole card in the window of a room, with the rest of the window being curtained off. It was by using a similar method that sunspots were first discovered and Sir Isaac Newton performed his experiments with prisms.
You can also use a telescope, adjusting the focus so that the image is clear on your "screen" for the required distance from the eyepiece. If your telescope is sufficiently powerful, you can get an excellent image that is large enough for you to be able to observe all the features of a total eclipse, including solar flares and "Baily's beads". It should go without saying that looking through the eyepiece to set up the telescope is a complete no-no!
The only total eclipse that has occurred in my lifetime in the United Kingdom was that of 11th August 1999. I had been looking forward to the event ever since childhood, as I had worked out, many years before the event, that the eclipse would mark my 47th birthday! Being in August, the whole family was able to take its annual holiday in Cornwall (the south-west corner of England) where the eclipse would be total at around 11.00am.
We had the telescope and screen ready in the garden of the cottage we had rented at a vastly inflated price, and hoped that the clouds would roll away in time. They didn't! We experienced everything else to do with the eclipse, such as the light fading, the streetlights coming on and the birds ceasing to sing, but the telescope showed us absolutely nothing. Then, as the light started to return, the clouds thinned just enough to allow us to see an excellent partial eclipse in perfect safety. We could have wished the cloud filter to have been at the right density a few minutes sooner, but that was not to be.
Fortunately, there were plenty of professional observers at work that day, in places where the clouds were not a problem and using sophisticated equipment, who were able to record the whole event and show us excellent television pictures, so the event was not lost to us totally. But there is nothing like seeing something at first hand for yourself, and one day I hope to be able to so exactly that, using the proper method of indirect observation, of course!