Smoke alarms usually work by optical detection, which means that they detect small changes in the light to identify smoke in the air, which then triggers an alarm. There are also ionisation smoke detectors, which produce ionisation in the air using a device called a radioisotope. This will again detect changes in the ionisation levels in the air caused by smoke, and will trigger an alarm. Some alarms are a combination of both optical and ionisation detectors.

Generally, an optical detector will find the early stages of a fire more quickly, as long as smoke is generated, while the ionisation type is more readily triggered by flame. The optical type is often recommended for home use, as they are better at detecting the kind of fires that often start in the home, eg smouldering fires caused by burning sofas.

You can find an overview of different smoke alarms and their uses here.