Could someone give a general outline of what the games does to increase the difficulty when playing King, Emperor and Deity?
Every increase in difficulty affects many different aspects, for example
However, probably the most significant change in the higher difficulty settings is the many boosts AI civs receive, which include
A more concrete example: playing in the Emperor difficulty means the AI starts with Pottery and Animal Husbandry researched; gets an extra warrior and a scout; units cost it only 75% of their worth; unhappiness is only at 85%; etc.
Personally, I feel disadvantaged the most at the early stages of the game, where you struggle desperately against every barbarian camp while they're dominating with their extra soldiers and reach new eras faster, not to mention getting all the wonders because of the production and technology boosts.
You can see a more precise listing of exact effects in the XML file