How does a field know when to make how many particles? Suppose I dump a certain amount of energy into a field. When does it make one particle and when does it make 2 with lower energies?
 A: You cannot just "dump energy" , you have to model with the interactions. 
Example.
The proton proton collider distributes the energy of the scatter according to quantum mechanical formulas, to the constituents of the protons (quarks and also the sea of quarks antiquark gluon) according to specific interactions , which have a probability of being expressed, since it is the quantum mechanical framework. This process has been modeled in the Monte Carlo simulation data, and the data fitted. Where there is a bump, i.e. the monte carlo has not predicted the shape, there is a discovery, as the Higgs discovery.

The straight lines under the bump are monte carlo background according to the model with various error  assumptions.
A: The energy in what form? Presumably, you are saying you collide certain particles with certain energies. Now, I'd do you one better, how do you know which field you are "dumping energy" into? Not just how many particles are made is the question, the question is what type of particles are made as a result of the scattering. So, you don't know. You can only calculate probabilities of all different outcome states using Feynman diagrams (which are) based on the Lagrangian of your theory.

$\small\text{Of course, this is a simplified answer with a weakly coupled theory in mind which admits}$
$\small\text{(a Lagrangian and) particle states, etc. }$
