Radioactive decay happens as an unstable nucleus - the parent nucleus - made of protons and neutrons attempts to reconfigure itself and become more stable, producing one or more daughter nuclei.
There are three main types of radioactive decay.
Alpha decay: An element with a proton or atomic number Z and nucleon or mass number A decays int a nucleus with proton or atomic number Z-2 and nucleon or mass number A-4, emitting an alpha particle with atomic number 2 and mass number 4.
e.g.
${}^{226}_{88}Ra \rightarrow {}^{222}_{86}Ra + {}^4_2 He$

Beta decay:
A neutron in the nucleus decays into a proton, electron and antineutrino, producing an element with the same mass number but one more proton.
e.g
${}^{113}_{53}I \rightarrow {}^{113}_{54} Xe+{}^0{-1} \beta + \bar{v}$

Gamma Emission:
An excited nucleus may become more stable by emitting a gamma ray. The nucleus is the same isotope as before the day, but less energetic and more stable.