Search for creation and anihilation operators in second quantization. It's quite simple. I give you a field with some particles populating some modes, and apply

Search for creation and anihilation operators in second quantization. It's quite simple. I give you a field with some particles populating some modes, and applying the creation (annihilation) operator gives you a field with one more (less) particle in a mode. That's how the game starts. If you're a particle physicist you typically develop this further into a system in terms of an action so you can use a path integral formulation, and then the action is written in terms of a Lagrangian Density, where you write the fields and their couplings. You typically then talk in the language of propagators (look for electron and photon propagators) and Feynman diagrams (which may be obtained from the Hamiltonian or Lagrangian) Condensed matter people and quantum opticians typically stick with the Hamiltonian (creation/annihilation) picture. Theories like superconductivity (BCS theory) are phrased like this. The standard model though is typically written in terms of the Lagrangian, though.