The basic building blocks of this device are a monochromatic light source, usually a laser, a detector, two mirrors and one semitransparent mirror. These are put together as shown in the figure.
mirror ------- | | semitransparent light | mirror source | / ---+ | / | | |/ | *--------------/-----------| mirror | /| | ---+ / | | / | | | +-|-+ | | | detector
Minuscule changes in the distance between either mirror and the semitransparent mirror will result in large changes in the amount of light energy the detector picks up.
An interferometer allows very precise distance measurements. By moving one mirror slowly away, the detector will show a regular decrease and increase of luminosity. The distance between two peaks in the detector corresponds exactly to one wavelength of the light used.
Of course, in Michelson's day, they didn't have lasers, so instead they used a gas discharge lamp, a filter, and a thin slot or pinhole to make more-or-less coherent? monochomatic? light.
In one version of the Michelson-Morley experiment, they even ran the interferometer off starlight.
Depending on your browser, it might not be obvious that the semitransparent mirror is at 45 degrees to the direction of the light beam. There are two paths from the light source to the detector. One reflects off the semi-transparent mirror, goes to the top mirror and then reflects back, goes through the semi-transparent mirror, to the detector. The other first goes through the semi-transparent mirror, to the mirror on the right, reflects back to the semi-transparent mirror, then reflects from the semi-transparent mirror into the detector.
If these two paths differ by a whole number (including 0) of wavelengths, there is constructive interference and a strong signal at the detector. If they differ by a whole number and a half wavelengths (eg, 0.5, 1.5, 2.5 ...) there is destructive interference and a weak signal.
There are many other types of interferometer. They all work on the same basic principles, but the geometry is different for the different types.