How are x-rays used to detect broken bones?

X-Rays are high energy photons, similar to light, but not visible to the human eye. These photons mostly pass through soft tissue, and are mostly absorbed by metals and semimetals. Therefore, the calcium of your bones absorbs much more of the X-Radiation than does your blood or other tissues.

The "Plate" is a transparent plastic sheet with chemicals on it. The chemicals turn dark when exposed to X-Radiation, which provides a negative image on the film. The chemicals are neutralized and fixed on the transparent plastic with other chemicals. This leaves the technician with the "Film", which is hung up on light boxes to highlight the image.

Often, a broken bone is obvious (a jagged line through an otherwise clean white bone), but sometimes a doctor uses their expert knowledge of physiology to detect less obvious fractures or connective tissue tears that may only look like shadows to the untrained eye.

Note that X-Radiation is ionizing. It is lower energy than nuclear radiation, but there are still limits to exposure. Often, a lead blanket will be used over parts of your body that may be exposed but shouldn't be, and the doctor or nurse will shield themselves to prevent daily, multiple exposures.

That being said, a couple of X-Rays in a year (dental, broken arm) are considered safe. Everyone is exposed to radiation all the time from the sun, natural water supplies, etc. It's only radiation in excess of what our bodies can process which is a problem.