Alpha- Loses 2 neutrons and 2 protons
Beta- Ratio of protons/neutrons changes
Gamma- No change in particles, but loses energy
Alpha decay involves the ejection of a helium nucleus, which is just two protons and two neutrons. This means that the atomic mass decreases by 4 and the atomic number decreases by two. This decay is typical of radioisotopes which have nuclei that are too large.
Beta decay involves the ejection of an electron or a positron. This happens when there is the wrong ratio of protons:neutrons in the nucleus, outside of what we call the 'zone of stability'. When the isotope has too many neutrons, neutrons eject an electron and become a proton. The atomic number thus increases by 1. When the isotope has too many protons, protons eject a positron and become a neutron. The atomic number thus decreases by 1.
Gamma decay is a release of energy- it never occurs alone and accompanies either alpha or gamma decay. The purpose of gamma decay is to release energy as nuclear particles are being rearranged.