The most important thing to keep in mind when viewing the Sun, including during a partial eclipse, is to never look at the Sun directly without proper viewing glasses. Sunglasses do not work -- you will damage your eyes permanently if you try to watch the eclipse with regular sunglasses.
One great way to view an eclipse or to see sunspots is through glasses made with special filters expressly designed for viewing the Sun. Such glasses are available at some science and astronomy stores. Or, get a piece of number 14 welder's glass from a welding supply store.
Being able to hold this up to your eye and look directly at the eclipse just gives people the most amount of satisfaction.
Test the glasses out in advance -- you can view the Sun on any day with these proper devices. But even with these special glasses, experts advise watching the Sun only for short periods of time.
If the glasses are at all damaged -- with scratches or holes in the protective coating -- do not use them.

Project the event
If you have no special glasses, don't despair. The next best approach (and a very simple one) is to project the Sun with a mirror.
Use a small mirror, like a makeup mirror, says Espenak. With masking tape, cover all but about a 1/2" square in the center of the mirror. Then hold the mirror at an angle and project the Sun onto a shaded wall or into a garage.
That works well for eclipses. For sunspots, there are other methods.

Pinhole camera
Another simple -- and safe -- method of viewing an eclipse is to create a simple version of what's called a pinhole camera.
Start with two pieces of white paper, poke a small hole in one with a pencil or pen. Let sunlight go through that hole and fall onto the second piece of paper, held a foot or two below the first, in its shadow.
You will see a tiny, round image of the Sun and can follow the progress of the eclipse.
Again, do not look through the pinhole directly at the Sun.

Binoculars
If you have a pair of binoculars, you can combine the pinhole and projection ideas, either for seeing an eclipse or detecting sunspots. Of course, never look at the Sun directly through the binoculars. Duncan explains this method:
Take a piece of white paper, and have someone hold it about 1 foot (0.3 meter) behind the eyepiece of the binoculars. Point the binoculars towards the Sun. An image of the sun will come out the eyepiece of the binoculars and shine on the paper just like an overhead projector shines onto a screen. Adjust the binocular focus until the image of the sun has a sharp, not fuzzy, edge.
The binoculars on a table to hold them steady. Or attach them to a photographer's tripod. Using this method, sunspots may also be visible -- as dark areas -- on the projected image.