The radiation from a radioactive sources is usually in the form of alpha particles, beta particles and gamma particles.
There are several methods of detecting these forms of radiation which differ based on the effects that the radiation have on different substances.
The most widely used apparatus is called a Geiger counter. This works on the principle that when a radioactive particle or a photon passes through an inert gas, the gas becomes conductive. Electronic detectors are able to measure this change in conductivity and detect the level of radiation. The apparatus can be made more sensitive to a particular form of radiation by choosing an appropriate gas or similar substance that changes conductivity when struck by radiation.
Another apparatus is a scintillation counter. Here, the detector is a substance called a phosphor that gives off light when struck by particles of radiation. The light is detected using an electronic circuit and based on the number of particles that strike the phosphor and their energy, is able to give an estimate of the level of radiation.