The hand reading thought process begins way before showdown; it begins at the start of the hand of even earlier if you include tells and table image. As actions occur, we can then narrow down the range of likely hands our opponent holds - this thinking process is used by all good hand readers; they think in terms of ranges instead of specific hands.
You make an educated guess on a flush or not based on how the betting went, possible tells, and details like this. You will never really know for sure, but you will make better informed decisions if you eliminated what hands you don't think they hold. When did they show aggression? Were they passive until the River as the Flush came in? If you bet bigger once or twice before the River, and they called, then that is basically saying: "I got something." Maybe a pair or Flush draw, but what exactly depends on the player and their play style too.
Fair enough, you can't always play with the luxury of a bigger chip stack. Always enter those situations with some caution though - we must always consider the option of them going All-in and forcing us to fold. If they shove often, and keep forcing you to fold, then adapt by playing back at them earlier or by tightening up your preflop range so you have the confidence to call off an All-In shove. What you don't want is to be having cards with good potential (like KJo or JTs) and then constantly be forced to fold. Perhaps a little research into "effective stacks" might be worth looking into.
lol This is not exactly untrue in many situations
Taking it a step further without the humor, what does their decision mean? Say they call our pot sized bet. That is on the larger size for sure, a maniac might bluff All-In over you if they think it will work enough; meanwhile a nit in the identical spot will always fold out the worst draws and only continue with the best made hands. A lot of hand reading is trying to reason more-or-less how everyone else thinks. Just because calling in a certain spot isn't something you would do (might not even be a profitable call), that doesn't mean the opponent reasons the same way.
Careful here! Some board textures will ONLY get you called with better hands than yours. What is the purpose of our betting? Is it a thin value bet? Is it trying to induce a fold from a better hand? Is it trying to provoke a bluff? etc. We must know why we are betting.
Let us assume the board is Ah Ks Kc 9h 2h
(Ace of hearts, King of spades, King of clubs, 9 of hearts, 2 of hearts)
By the end of the River, the heart Flush got there, the pair of Kings gives better Full House possibilities and so on. Let us assume we hold pocket 8's (say 8s 8c). What hands do we beat? If our opponent called 1,000 chip bet somewhere then they probably have something if they are a reasonable opponent. What hands would ours beat? No Ace-high hands because an Ace would have paired on the Flop and reasoning like this. If we raise like 5,000 on the River, then what would they possibly call that with? Probably a Full House or Ace with a good kicker - maybe even a good Flush if you bet big on the end, but even a Flush has to worry about a hand like AK making a Full House. Betting bigger isn't always useful - sometimes a more modest bet gets just as many folds and you won't be losing as much when they do call.
Flopping 2-pair is a great hand, but everything depends on other factors in poker it seems. This might be a good play to go All-In with a Flopped 2-pair if the chips stacks are shallow enough. Flopped 2-pair with 10 Big Blinds (bbs) in my stack? Going All-In is justifiable. Going All-In with 2-pair on the first hand of a deep stacked game (maybe 100 bbs) seems suicidal. Who will call that? Someone with pocket Aces or someone thinking you are a maniac who bluffs too much. Most of the time, this bluff will work but the one time you do get caught, it will probably more than lose what few chips everyone folding thus far in the game added up to.