How detailed should a methodology be presented? I am writing a manuscript dedicated to the classification of natural processes occurring worldwide. In this study, I create a composite model involving a classifier, i.e. a Neural Network model, that will be used to process the classification. The study discusses which variables, related to the observed natural processes, are more important for the classification procedure (e.g., weight matrices are described and discussed).

To explain the method, I briefly give an overview of machine learning (principles) in 3 sentences and relate it to my study. In addition, I also explain what are neural networks, and the explanation is made in the appendix (3 pages). For both, machine learning and neural network, I use a citation pointing directly to a book.

Is it preferable to leave a citation inside my manuscript so that the reviewer just takes a look at the cited book to understand how neural networks work, or can I explain the concept in the appendix (but in this case I use different citations for detailing the explanations)?
This is extremely dependent upon the journal you are submitting to (and who the audience of that journal is) and the roll of the dice on who your reviewers will be. Where one reviewer believes that it is critical to demonstrate that you have met your assumptions for regression with the inclusion of residual plots and formal tests, another (and equally as qualified) will state that such inclusions only add clutter to the methods. And finally, you might have an editor come in and say that it should be included but moved as an addendum. Even scanning prior journal articles is not always the best indicator (though its a very good one) because editors change and reviewers are different. 

Your best bet is to go with what you feel is correct and allows for the clearest replication of your methods. If this involves going into the mechanics of back propagation and what a sigmoid is, then so be it. If, as you have stated, that you feel that a reference will suffice, then thats ok as well. 

To give an example, I have two papers coming out this fall where-in both use the same method to calculate a statistic. Paper one, the reviewer felt that I should explain, in detail, how that statistic is calculated due to probable reader unfamiliarity. In paper two, the reviewer accepted the simple citation of "this statistic was calculated in the manner described in _____(XXXX)". 

So, in summation, it depends, and you should use your educated determination as someone with knowledge of the literature to guide you.