Resources for learning the technical parts of atmospheric modeling
For fundamentals on numerical methods applied in atmosphere and ocean modeling, see the GARP publication by Mesinger and Arakawa: Numerical Methods Used in Atmospheric Models. This old, but certainly not outdated text provides the basics on time and space discretization and stability, with particular focus on solving advection equations, and gravity-inertia wave (read: shallow water) equations, and is relatively easy to digest. A must read for any meteorologist or oceanographer using or developing numerical models.

Then, an excellent textbook by Dale Durran, Numerical Methods for Fluid Dynamics: with Applications in Geophysics maintains similar application focus as Mesinger and Arakawa, but expanded with more numerical algorithms and in-depth analysis. It covers the basics as well, so it can be used as a stand-alone text.  

There are many other more general CFD textbooks that contain material applicable to ocean and atmosphere modeling. The majority are more geared towards mechanical engineering applications, so you may need to apply a filter (hur hur).

On the other hand, if you are more interested in physics parameterization schemes used in atmosphere models, such as cumulus convection, microphysics, or boundary layer parameterization schemes, a book by David Stensrud, Parameterization Schemes: Keys to Understanding Numerical Weather Prediction Models, is an excellent summary of current state-of-the-art. It covers a wide area of unresolved physical processes in the atmosphere, so it does not go into too many details - if you are interested in fully understanding a particular scheme, you will need to follow the reference chain and read the particular papers on the topic. I highly recommend this one if you are interested in gaining an overall understanding of parameterizing atmospheric physics processes.