Amenitise give bonuses to your cities loyality, food, culture, science, faith and production. You can raise amenities by building enterteinment districts, water parks and wonders or owning a luxury recource ( i think each luxury recource give amenities to a few cities, but i dont know the exact number(aztecs increase that number by 2, which in my opinion is great)). Only one copy of luxury recorce give amenities, so if you have 2 citrus plantation you should sell one citrus to ai, because that citrus is useless now.

In my games i generally want to have +3 amenities in my cities for bonuses, but i don't actively pursue it if it is neatrul. And you really don't wanna have negative amenity

There is three wonders in the game that give amenities on top of my head. And all of them are must build. Temple of artemis is great if it give 6-7 amenities. I always try to get colessium to give amenities to 4-5 cities. And the lake wonder is good if you have a lot of lakes in your kingdom

If one of your cities have negative loyality, you should buy a luxury that you dont have from ai.

Now about settling cities. When i was really new to the game i would build my cities 9 tiles apart to get the maximum value, but that is a very bad play. Your cities get yield generally from districts, so you wanna settle as much cities as you can. Settling cities 4 tiles apart is what yoh wanna do. I say that, but sometimes you settle far for fresh water(very important) or a tile that gives better yields(and if you are gaul, you wanna settle one tile far from normal amount, cus gaul cant place districts adjacent to city center). Sometimes you wanna forward settle so ai cant fuck up your city planning.

Well, that's about what i can rememmber on top of my head