The particles and the forces
Every kind of decay is just a nucleus rearranging itself. To follow them you need to know what a nucleus is made of and which forces act inside it.
Zooming in: atom → nucleus → protons & neutrons → quarks
If the nucleus were a marble, the electron cloud would be about the size of a football stadium, yet the marble holds 99.97% of the mass. The squiggly grey lines are gluons, which hold the quarks together.
The cast of characters
These are all the particles you'll see in the decays. Some are matter particles (balls in the diagrams). Others are force carriers (wavy lines): particles that get passed between other particles, and that passing is the force.
The three forces fighting inside a nucleus
Strong force
Attracts. Enormously strong, but very short-range: it only reaches about one proton-width (10⁻¹⁵ m), so each nucleon grips only the ones touching it. It locks quarks inside protons and neutrons, and its leftover grip holds the nucleus together.
Electromagnetic
Like charges repel, and the reach is unlimited. Every proton pushes on every other proton in the nucleus, even ones on the far side. Up close it's weaker than the strong force, but in a big nucleus all that pushing adds up. Carried by photons.
Weak force
Hardly pushes or pulls at all. What it can do, and nothing else can, is change a quark's type (down ↔ up). That turns a neutron into a proton or back, and it creates electrons, positrons and neutrinos along the way. Carried by W bosons.
Gravity is also there but it's about 10³⁶ times too weak to matter inside a nucleus.