How do alpha particles decay?
They don’t. Only nuclei heavier than iron decay spontaneously.
Rather α particles are produced when other nuclei decay and emit one or more α particles. This process is called α decay.
For example, uranium-238 decays through α-particle emission to form thorium-234 according to the equation:
₉₂²³⁸U → ₉₀²³⁴Th + ₂⁴He