Question

From your experience, predict which of the following reactions are spontaneous.
a) Zn(s) + 2H+(aq)--> Zn+2(aq) + H2 (g)
b) CaCO3(s) + 2H2O(l) --> Ca(OH)2(s) + H2CO3(aq)
c) CH4(g) + O2(g) --> CO2(g) + 2H2O(g)
d) Ag+(aq) + Cl-(aq) --> AgCl (s)

Our book spends very little time talking about spontaneity. How would I predict whether or not a reaction is spontaneous?

It depends on what you know.

If you know about Gibbs Free Energy, the answer is there.

If you considered change in Enthalpy, a positive change of Enthalpy is a strong indication of spontaniety.

If you have experience with reactions, you have a strong sense. For instance, the combustion reaction c) releases a of heat, and could be spontaneous if it were at a high enough pressure or temperature.
Reaction b: the reverse reaction is an acid base reaction, which is spontaneous.
a: anyone who has dipped zinc into acid knows the answer to this.
d_ Solver chloride does precipitate

Given time, you will have experinece to "know" the answers..