Putting players on hands relies I think on two areas - observation and experience.
Observing the player means watching the hands they play and dont play. Pretty quickly you can put players as one of the four basic greoups - Loose/Tight & passive/agressive and have at least an idea of their starting hands and postflop game.
another part of observation is to remember their action in the specific hand, players action in a hand will usually follow a certain logical pattern

The rest is common sense and experience.