How to use a QUEST staircase in 2-AFC? Firstly, I need to declare that I am not psychologyst, however I am currently working on visual recognition research. To be precise, I working on face recognition deficits in Autism Spectrum Disorder. I am in charge of doing an experiment but I feel I come to a dead end even though I didn't even start with it.

As I mentioned above, I investigate face recognition deficits in ASD. I will use faces and objects. For this task I will use 2-AFC match-to-sample task. I need to morph faces and objects and for this purpose I need to use a QUEST staircase for measure morph distance at which participants could discriminate between items with 75% accuracy. 

Here is the problem: I don't know how to use a QUEST staircase. Or better say, I don't know how can I decide how many trials should I have, which morph distance should I use between items, how should I know which morph distracter should I use, should I use in the beginning easy test pairs and what exactly does it  means, is 85%-morph distracter is an easy pair, etc.? As you can see I don't know to do an experiment, it is almost completely new field for me. 

I am trying to find my answers in: Psychophysics: A Practical Introduction by   Kingdom &amp; Prins; Experimental Design by Cunningham &amp; Wallraven; Visual Psychophysics by Lu &amp; Dosher just to mention a few. However, I wish to find some book or article where I can see an example step by step how to make a similar experiment, i.e. AFC. I know there is bunch of information but I am just overwhelmed and lost.

What literature/ web sites/ blogs etc. can you suggest to me? How/ where to start?
There is a lot going on in your question. QUEST, as well as many other adaptive procedures, is well suited for a task like estimating morph distance in a 2-AFC paradigm. There are, however, a couple of points in your question, that make me think QUEST is not a good paradigm.

The QUEST paradigm is designed around setting the signal level to find the the "sweet point" of the psychometric function (something like the signal level that maximizes the Fisher Information). I am not aware of any psychometric function that has a sweet point of 75% correct (most are 90+ percent correct).

The second issue, is you mention a fixed number of trials. Typically, QUEST is used with a stopping rule that specifies the expected variance of the estimate (i.e., you run enough trials until the CI on the estimated threshold is small enough).

The easiest way to run these types of experiments is to use software written by someone else (that you trust). Pelli was involved in the early development of both the QUEST procedure and the Psych Toolbox for MATLAB/Octave. The Python based PsychoPy also provides the QUEST procedure and is commonly used.