You are asking for an introductory survey of what is called string phenomenology
First a reference, then some comments:
One book collection which goes at least a long way towards providing a survey of which aspects of string theory map to which aspects of the standard model in the low energy effective theory is this here:
(Let me know if you don't know how to get an electronic copy from this data...)
In there, the lectures closest to being dictionary-like are probably these courses:
- Course 1: Topics in string phenomenology by Antoniadis
- Course 2: Orientifolds, and the search for the Standard Model in string theory by Kiritsis
- Course 7: The standard model from D-branes in string theory by Uranga
- Course 12: Lectures on constructing string vacua by Denef
Now the comment: there are MANY ways in which quantum field theory arises inside string theory. String theory is like a huge dictionary of QFTs mapping out a large part of their moduli space, and connecting them in ways ("dualities", "geometric engineering") which are non-obvious from the point of view of just QFT. String theory is to QFT as complex analysis is to real analysis: a larger space in which all the relations in the smaller space become manifest.
In particular there are many different ways for string model building. The relation between CY Euler characteristic and SM generations in the above question arises only in one class of them, namely in the traditional heterotic model building. This is the class of string models with the longest history.
But in recent years other classes have found much attention, notably models of intersecting branes in type II. Here the "dictionary" is a very different one, but is very beautiful, too: all the properties of the standard model are encoded in the precise geometry of intersecting branes with open strings on them.
Then there is M-theory model building and more. Of course all these are related by duality.
And one well-kept truth is the following: this huge collection of models that have been discussed in the literature is certainly just the tip of the iceberg, this is just what is easiest to describe!
In particular, the bulk of model building in existing literature works and argues with fairly classical geometry, with string sigma-models built from differential geometric target spaces.
But abstractly a perturbative string vacuum is any 2d SCFT of central charge 15. "Most" of these will not be geometric at all, at least not in the compact dimensions. Very very little has been studied of this large moduli space of 2d SCFTs. All of the models currently under discussion may be too naive simply because they start geometrically.
To amplify this: there is a systematic way to take the point particle limit of a 2d SCFT (see the reference here ) and the result is... a spectral triple. Abstractly speaking, that relation is the "true dictionary" between string theory and point particle QFT. And spectral triples, as you know, generically do not describe "geoemtric" backgrounds, that's their whole point.