The only thing I would add, is to first read about the basics of how an a/c system is supposed to work. Like anything - if you do not know what it is supposed to do then you won't know where to begin looking. NO MAJIC WANDS. Here is a quick basic theory. 1) Most everything will change (as temps. go up solid, to liquid, to gas of course as it cools the opposite; gas, liquid, solid) 2) engineers found a chemical that would do this quickly - called FREON. 3) Most everything also wants to be warm (not hot or cold) that is why they designed it to be adjustable! 4) Freon also wants this, and Pressure and temperature are cost to the same - at least for this quick class. In an A/c system it is never cold enough to freeze (solid)! for the sack of basic lets say we use 30psi as it's liquid state, and 250 as a gas. As stated, we will talk about this as temps. 30psi = 30 degrees etc. 200 - 400 psi = 200-400 degrees, etc. 5) the mechanical parts of the A/C cause these things to happen inside the system itself (orifice tube, evaporator, compressor, condenser, accumulator, etc. you need to research this part) Freon is sent into the dashboard as a liquid- in fact the compressor pushes it around the system - plus or things ( so it is about the 30-degree area) It wants to be warn so it takes the heat from the interior and starts to become a gas as it does it is pushed out of the interior towards the condenser, by the time it gets there it is now all gas and the compressor compressed it to 300-400psi/ degrees. It's a hot day in you area 105degrees in the shade BUT the freon is 300 plus PSI (or degrees) so the 105 air temp outside says I want to be warm also!!!!~ so it steals the heat that the freon sucked out of your interior, so it cools down and heads for the dashboard again - becomes a liquid (because of an orifice tube or expansion valve etc.).
So in order to diagnose you need to know the parts on your vehicle, have tools to read those pressures at specific places in that system. Diagnose the electrical functions of the controls and parts in that system.
Get an understanding of what is supposed to do so you can see what it is not doing. The fix part of the problem is usually easier, than the diagnoses. Not meant to be sarcastic but it is like saying I have a flat tire what is wrong.
PS inexpensive tools can be had at places like Harbor Freight.