I read something about nuclear decay as being a reaction with no activation energies. Why is this so, and how does this work?
You're asking too much. I can answer you in short:
Nuclear Decay Reactions occur when the nuclear force$^1$ between nucleons is not able to hold the nucleons together.
Now as it can't hold large nucleons, the nucleus starts emitting particles or following special processes to reduce mass or nucleons and reach a stable zone, the choice of process depends on where the nucleon is as per a graph $^3$.
$^1$.one of the four fundamental forces of nature. If there was no nuclear force, everything would repel apart. The reason being, if there was only electrostatic force between protons, the whole nucleus$^{1a}$ would repel away. So another "nuclear force", acts into play, which is blind to the charges, and acts according to another intrinsic property$^{1b}$ called color$^{1c}$ .
So now when nucleons are at the order of 1 fermi$^{1d}$ , the force is attractive and stops acting very (very) quickly (dying).
$^{1a}$ actually, only protons, to be specific
$^{1b}$ like mass, charge, etc.
$^{1c}$ and involves variety of particles called gluons, mesons, hyper-mesons, quarks, etc.
$^{1d}$ named after great scientist, $1$ fm$=10^{-15}$ m
$^{2}$$\beta^-,\beta^+,\ce{_2^4He}(\alpha)$, K-capture etc.
$^3$ which predicts that is no. of protons = no. of neutrons, then nucleus is stable ,generally, only for lighter nucleus(es) and for heavier ones it bends a little upward like a parabola ($y=x^2$)