How Smoke Detectors Work
Smoke detectors are one of those amazing inventions that, because of mass production, cost practically nothing. Smoke detectors save thousands of lives each year. It is recommended that every home have one smoke detector per floor. We will look at the two most common types of smoke detectors used today.
All smoke detectors consist of two basic parts: a sensor to sense the smoke and a very loud electronic horn to wake people up. Smoke detectors can run off of a 9-volt battery or 120 volt house current.
Photoelectric Detectors
Occasionally you will walk into a store and a bell will go off as you cross the threshold. If you look you will often notice that a photo beam detector is being used. Near the door on one side of the store is a light (either a white light and a lens, or a low-power laser), and on the other side is a photodetector that can "see" the light. When you cross the beam of light you block it. The photodetector senses the lack of light and triggers a bell. You can imagine that this same sensor could act as a smoke detector. If it ever got smoky enough in the store to block the light beam sufficiently, the bell would go off! There are two problems: 1) it's a pretty big smoke detector, and 2) it is not very sensitive. There would have to be a LOT of smoke before the alarm would go off - the smoke would have to be thick enough to completely block out the light, and that's a lot of smoke.
Photoelectric smoke detectors therefore use light in a different way. Inside the smoke detector there is a light and a sensor, but they are at 90 degree angles to one another, like this:
In the normal case, the light from the light source on the left shoots straight across and misses the sensor. When smoke enters the chamber, however, the smoke particles scatter the light and some amount of light hits the sensor:
The sensor then sets off the horn in the smoke detector.
Photoelectric detectors are better at sensing smoky fires, such as a smouldering mattress (burns slowly at a low heat without flames).
Ionization Detectors
Ionization smoke detectors use an ionization chamber and a source of ionizing radiation to detect smoke. This type of smoke detector is more common because it is inexpensive and better at detecting smaller amounts of smoke produced by flaming fires.
Inside an ionization detector is a small amount of Americium-241 (perhaps 1/5000th of a gram). The radioactive element Americium has a half-life of 432 years, and is a good source of alpha particles. Another way to talk about the amount of Americium in the detector is to say that a typical detector contains 0.9 microcurie of Americium-241. A curie is a unit of measure for nuclear material. If you are holding a curie of something in your hand, you are holding an amount of material that undergoes 37,000,000,000 nuclear transformations per second. Generally that means that 37,000,000,000 atoms in the sample are decaying and emitting a particle of nuclear radiation (such as an alpha particle) per second. One gram of of the element radium generates approximately one curie of activity (Marie Curie, the woman after whom the curie is named, did much of her research using radium).
An ioniziation chamber is very simple. It consists of 2 plates with a voltage across them, along with a radioactive source of ionizing radiation, like this:
When smoke enters the ionization chamber it disrupts this current - the smoke particles attach to the ions and neutralize them. The smoke detector senses the drop in current between the plates and sets off the horn.
Speaking of alarms, whenever the words "nuclear radiation" are used it often sets off an alarm in many people's minds. The amount of radiation in a smoke detector is extremely small. It is also predominantly alpha radiation. Alpha radiation cannot penetrate a sheet of paper, and it is blocked by several centimeters of air. The danger the Americium in the smoke detector would pose can only occur if you inhale the Americium. Therefore you do not want to be playing with the Americium in a smoke detector, poking at it, or disturbing it in any way, so that it does not become airborne.
Ionization detectors respond better to flaming fires.
Inside a Smoke Detector
You probably have a couple of smoke detectors in your house. When you take off the cover you find that a smoke detector is pretty simple. This one consists of a printed circuit board
an ionization chamber (the silver cylinder toward the top right in the following picture) and an electronic horn (the brass cylinder toward the bottom right in the following picture):

Here is a close-up of the board:
and the underside of the board:
The ionization chamber is an aluminum can containing the ionization source. You can see that the can has slots in it to allow air flow. The can itself acts as the negative plate of the ionization chamber.
Underneath the can is a ceramic holder that contains the positive plate of the ionization chamber. Under that plate is the ionization source, WHICH YOU WANT TO BE SURE TO NOT DISTURB.