You've probably heard that light seems sometimes like a particle, sometimes like a wave. (The most modern theory of light, called quantum electrodynamics, says that light is made up of particles called photons, which nevertheless "interfere" or intermingle rather like waves.)
Well, building an interferometer is a particularly dramatic and striking way to see some of the wave aspects of light. Just looking around normally, you can see various objects. They look smooth, and they have sharp edges. It seems that there's an unlimited amount of detail available; you could look at anything as closely as you wished, to see smaller and smaller detail.
In fact, that's not the case---there's a definite limit to how much detail you can see, and it's related to the wave nature of light. You can convince yourself of this by constructing some artificial pupils with a needle and some aluminum foil. (No, eye surgery will not be involved; let's leave that to the professionals.)
There are several materials that work well for pinholes. The basic requirement is a thin, opaque material that can be pierced cleanly. Here are the ones I've used:
Try to get the brass, since it doesn't "work-harden" as much as aluminum does. (I've heard that silver foil is even better; see if your jeweler will give you a piece.) But aluminum is fine.
Cut a piece of foil five or ten centimeters square, and get a bulletin-board pushpin or a sewing needle. Find a smooth surface, like a formica countertop or a piece of glass, and put the foil on the surface. (The smooth surface helps to make small, round pinholes.)
Now lightly "spin" the needle into the foil. You'll need a little practice to find the right pressure; we're aiming to make a very small hole, perhaps 0.1mm in diameter, much smaller than the thickness of the needle itself. Make several holes of varying sizes; make a few big holes also, by using paper or cardboard as a backing and pushing the needle a bit into the backing. Check the sizes by holding the foil up to the light---small holes will appear dim, larger ones bright.
Now look through the various pinholes by holding them close to your eye. (If you wear glasses, you can either just take them off, or hold the foil up to the lens.) You'll instantly notice that everything gets a lot dimmer. The reason is obvious---your normal pupil is perhaps 3 mm in diameter, but these pinholes are only 0.1 mm. The pinhole lets through a thousand times less light.
When you look through the very small pinholes, you may notice that things not only get dim, they get fuzzy. The smaller the pinhole, the fuzzier your surroundings. (If you improvise a Snellen chart, the ophthalmologist's chart with the big E and the lines of letters, you can estimate how your vision degrades with the pinhole size.) This is a bit mysterious; what could be causing it?
The basic answer is that there's a limited amount of information you can stuff through a small hole. If the hole is very small compared to the wavelength of light (which is the distance between successive "crests and valleys" of the light; for green light, it's 550 nanometers, or 0.00055 mm), then only a diffuse overall glow can make it through. As the hole gets bigger, it can transmit increasingly detailed images.
The general term for this modification of light as it passes an edge or a small aperture is diffraction. You may have heard of diffraction gratings, the mirrors with very fine lines that produce spectra.
By the way, don't be alarmed if you see various small semi-transparent spots in your field of view. These are normal; they are called "floaters", since they float in the transparent media of the eye chambers. They are pieces of cellular debris that aren't seen normally because their shadows on the retina are blurred by the large pupil. Also, if you squint and then unsquint, you can see the line that the film of tear fluid makes on your cornea.
For the rest of this, you'll need a small, bright source of light. Distant streetlights at night are best, but you can get results with a flashlight or penlight, provided it's at the opposite end of a darkened room, pointed at you. (If you go the penlight route, make a "mask" of foil that covers the light except for a small hole, say 1mm.) You want a brilliant, pointlike "star".
Now view this star through the various pinholes. As before, small pinholes will give a largish patch of light where the star used to be, and larger pinholes will give smaller patches. You will also see rings around the bright central patch. This famous "diffraction pattern" is called the Airy disk, after a British scientist.
Now comes magic. Start making sets of two pinholes, closely spaced, a bit larger than the smallest you can make; you want a pinhole size that gives an extended patch of light in the star test above. (Mine are about 0.08 mm in diameter.) Space them about 0.5 mm apart, roughly the thickness of a fingernail, or the diameter of your needle. Again, though, vary the spacing from, say, 0.3 mm (these will be very close) to 1.5 mm. Also, you want them close to the same size, which you can judge by holding up to the light.
When you view the star through the double pinhole (wear your glasses for this), you will see an amazing set of lines or "fringes" that cross the Airy disk. (If the fringes don't appear, the star needs to be smaller/farther away, or the spacing is too large, or the pinholes themselves are too large.) Try rotating the foil; what is the relationship between the fringes and the direction of the line connecting the two holes?
What is happening here? The thing you'd expect to see would be two spots, or perhaps a single spot twice as bright as with the single pinhole. There is a single spot, all right, yet the fringes that cross it are completely dark in places, and actually four times as bright as before in their centers (this does make some sense, since things average out to the twice-as-bright case you'd naively expect with two holes).
The dark fringes are where the two pinhole-beams cancel one another out, and the bright fringes are where the beams reinforce one another. Similar things happen with water waves, or waves on a taut rope, or sound waves, but those probably seem a bit more ordinary to you!
Why doesn't this kind of thing happen all the time? It does; but most light sources, like the Sun or a flashlight, are not "coherent" or synchronized---this makes the fringes jump around far too quickly to see, and so they blur away into smooth objects. The small pinholes, and the large distance to the light source, have tricked the light into becoming coherent between the two pinholes, so that interference can be clearly seen.
You'll notice that wide hole spacings give fringes that are close together, until they are so fine they're no longer visible. My best pair gives about six beautifully distinct fringes in the center patch of the Airy disk. If you've got a really good star, you can see fringes in the faint rings as well.
If you're myopic (nearsighted), as I am, try using the two-pinhole foil without your glasses. Instead of a single Airy disk with fringes, you'll see two Airy disks somewhat separated, either with or without fringes between them. Why?
Make a three-beam or four-beam instrument with several pinholes arranged in a line. The fringes should get sharper, more distinct (why?). (It's difficult to space them equally.) Try adding another hole to the two-hole pattern, to make a triangle; how can you explain the resulting bizarre pattern?
One final remark. As I mentioned at the start, our best notion of light at the moment really is particles. Individual photons can be counted; they exist. Yet the dark fringes represent regions for which, with one pinhole, there is light, and with two, no light. Opening up another hole has prevented the particles from reaching the dark fringe! Do the particles "sniff out" the various routes to decide what to do? The full theory describes all these phenomena, so there is an "explanation" that works well, but the interpretation can be tricky (and, indeed, is controversial to this day). Other particles you may have heard about, like electrons and quarks, also behave this way; it seems to be a general rule that everything does.
If you're curious about photons and quantum behavior, there's a superb nontechnical book by Feynman called QED; The Strange Theory of Light and Matter. This book can be read by anybody, yet it will give you the unvarnished, real story about quantum field theory, from one of the original developers of the subject.