The first experiment in our book Nuclear Radiation with Vernier (NRV, discontinued) is all about this subject. Details and the table of contents can be found at https://www.vernier.com/nrv

The following is an excerpt from Nuclear Radiation with Vernier:

To determine the type of radiation (alpha, beta or gamma), first determine the background count rate, then the source count rate with no absorber. Next, place a sheet of paper between the source and the monitor. If the counts are significantly reduced, the source emits alpha particles. If the count rate is not significantly reduced, place a 2 mm thick sheet of aluminum between the source and the monitor. If the count rate goes almost to the background level, the source is emitting beta particles. If the count rate is only reduced, the source is a gamma source.