Assuming you have GS and RF DLCs.

• trading earns food and production that isn’t taken away from the destination city.
• For builders do the recommended thing (edit to clarify: choose the resources you want and ignore the map icons, that just shows what is closest, but once you're on the resource build the recommended thing that it says), for science researches and culture civics try to hit the inspirations where you can before researching, and with city production do whatever the hell you want, screw the recommendations.
• To build wide or to build tall are two different strategies. I think 4 cities is good for the tall strategy, lots of cities if wide but watch that your people are happy (aim to develop new kinds of luxury resources with your Builder units or trade ones you have extra with what your enemies have extra but you don't have). Settling quickly is good, just don't overextend lest you get screwed by barbarian or an AI or player who sees a good opportunity to war you.
• AI trading gives you more favourable trades when in a good relationship and terrible trades if they denounce you. Often times you can snag open borders for 1 coin even in neutral. The main thing you want to trade is spare luxury resource for spare luxury resource like I said.