[FMDenaro]

The old book of Morton can be a starting point, then many modern books of CFD explain the essence of FDM (Anderson, Pletcher, Hirsch, Peric, etc.).

Speaking in general:

explicit FD: are based on a Lagrange polynomial, therefore higher order derivatives require larger computational stencil

implicit (Compact) FD: are based on the Padè interpolation, you can get high order derivative on compact stencil at the price of solving a linear algebric system.

Each term in the PDE is substituted by some FD formula to get a discrete equation that, depending on the PDE, is solved in direct/iterative way.