The easiest way for me to do this was memorize the "chemical equation (?) for each, showing how they decay.
Alpha Decay: The nucleus loses a Helium atom. So Atomic mass decreased by 4, and atomic number decreases by 2.
Beta Decay: Beta decay involves an electron. In Beta positive decay you form a proton and lose a neutron. This is because a neutron breaks down into a proton, electron and anti neutrino. Your mass number stays the same, and the atomic number increases by 1 (one more proton). You also release an electron and an anti neutrino.
In Beta negative decay, you lose a proton, so the mass number remains constant and the atomic number decreases by 1. A proton becomes a neutron, a positron, and a neutrino.
EK also discusses electron capture and positron emission. These are both forms of Beta decay. In electron capture a orbital electron and a proton form a neutron. You do not form an ion, because the atom has lost both an electron and a proton.
In positron emission a proton forms when a neutron is broken down into a proton, positron and neutrino.
Gamma decay does not involve the loss of any nucleons. In Gamma decay, an excited proton releases a high energy photon. This is the Gamma particle that is released. Alpha or Beta decay can result in Gamma decay.