Pinhole projection is certainly the safest and cheapest way to view the partial phases of a solar eclipse.
On one of the narrow ends of a shoebox (panel 1), cut two openings (about 1.5 cm across) as far apart as possible from each other, about 1 cm from the edge of the box (2+3). Cover one of the openings with a piece of aluminum foil and tape it in place (4+5). Next, punch a tiny hole in the foil using a fine nail, a pin or a sewing needle (6). The smaller the pinhole, the sharper (but fainter the projected image. Lastly, place a sheet of white paper (7) inside the box, on the opposite face from the pinhole: this will be your projection screen (8). The second opening will allow you to look inside the box at the small projected image of the sun, without letting in too much stray light. Put the lid back in place and seal off all remaining cracks and openings, except the ones that you cut in the first step.
Turn your back to the sun, and aim the pinhole at the sun while looking into the box, until you see the projected image of the sun on the screen (9). This “eclipse box” is very easy to make, and will show the changing shape of the “solar crescent” as the eclipse progresses. The projected image is rather small, but this method is perfectly safe since you are not directly looking at the sun.
There is a similar method that allows many persons too see the image simultaneously. Slip a pocket mirror in an envelope in which you’ve made a single hole using a paper punch. Point the mirror at the sun and direct the reflected beam of light at a white surface, preferably in the shade. The larger the distance, the bigger (but fainter) the image of the sun becomes. Even better, direct the sunbeam through an open window and project the image of the eclipsed sun on the wall of a darkened room.
During the partial phases of the eclipse, don’t forget to look around you: every small opening becomes a pinhole. For instance, sunlight filtering through the foliage of a tree projects hundreds of crescents on the ground! You can also make small openings between your crossed fingers, or use household objects such as a colander or a perforated ladle.
Another fun way to see the changing sun is to write a message in large letters on a piece of thin cardboard (a cereal box is perfect material for this); then, using a sharp pencil, punch a series of holes tracing out the letters (leave about 1 cm between holes.) During the eclipse, you can project your message on any uniform surface you want, and take a photo. Use your imagination, and have fun!