Start placing yourself into the shoes of others, whether they be animate or inanimate.
Thanks for the advice, especially the "inanimate".
Strategy games are good for exercising intuition
I researched strategy games a month ago for this purpose and ended up with: Go and X-Com. Anyone?
Martial arts which incorporate sparring e.g. Boxing, Muay Thai, MMA etc. where you are forced to read body language, read signs and outsmart your opponent (otherwise you get hit)
Reading signs and language, that's it! The "soft stuff" which engages intuition, but incomprehensible for logic. Like hands on clay.
Watching films and paying attention to the plot. Try reading the situation to see what comes next, ask yourself if the screenplay writer could of changed or added anything to the plot.
I do this naturally, seeing the future developments. But what I have forgotten is that "asking if the writer could have changed or added anything to the plot". I used to do that naturally, too, usually seeing "rail track schematics".
Acting; join your local theater club or when you watch a film or read a book try acting out how you would respond to a certain situation that the character is in, try connecting with the character and becoming the character.
Damn, I have really neglected a few ways of thinking.