WillStealYourUsername has already given a very good overview, to add to that...
It is a highly individual process and while many trans people share certain experiences, no two trans people will have exactly the same kind of journey.
While the public perception of trans people is very much focused on the rather rare cases of young children who will insist on being trans from an early age on. While these cases definitely exist, far more trans people are going through a gradual process of realization. There may be a final "egg crack" (the moment of final realization), but it is usually preceded by a slow process of smaller realizations and it is nowhere near a linear process...
As WillStealYourUsername describes so well, in hindsight all the signs and individual quirks make sense, but most people have to attain a certain level of self-acceptance before being able to recognize the various symptoms for what they are.
In my personal case, it was an intense jealousy of fem people that would never go away and culminated in a moment where I had an emotional meltdown over a fictional character who transitioned from male to female in their storyline. That's when I finally realized that I could do the same thing if I got my shit together and accepted being trans.