1st thing a city needs is enough food to get growing, so look for 1 good or 1 decent food ressources. Grassland Corn and Pigs are good, Fish is also, rest is decent (like plain wheat, grassland rice, bananas, clam, crab etc.). Also consider Floodplaines as a decent food ressource, if there are at least 2-3 of them.
Normally one would avoid settling on the ressources, though settling on the ressources is awesome in early game, as you get +1 hammer from settling on Marble, Stone or even Elephants and +1 food from many food ressources, fastening up the production or growth of your capital city significantly, so think about moving the settler if you see these kinds of ressources. Plain Hills also give +1 hammer, riverside luxury ressources give +3 commerce if being settled on, giving you a better shot at getting an early religion.
Best start to get is imho a plain hill with Marble next to a riverside gold giving you +2 hammers +3 commerce but that's so rare, I got it in 1 of 500 starts.
Followup cities should be placed besides river or any fresh water source if possible OR if needed AND besides strategic ressources like horses or copper. Levees apear so late, game is usually over by that time, but you still want to be able to build some farms if the city doesn't have enough food or if you want to speed up the growth of your Slavery shattered population.
Early production cities normally have lots of hills and ressources like Horses, Cows, Marlbe, Stone or Elephants, all of them giving + hamers. Commerce Cities usually have ressources like Gems, Gold, Silver, Fur, or later on the Calendar ressources like Silk, Dyes and so on. Aim for the early ressources first though, as it is a long way to calendar. Main thing again is food though.
One city needs more food than any city, so take the city with the most food to work specialists, thats your great Persons farm. 2 food is ok, 3 is decent, 4 is awesome for this kind of city. If it also has some hills and forrests, even more awesome, as you will be able to get wonders in that city giving you even more great person points.
Things you should never do:
Settle a City at a place where there is no food (exception to that is, if you wanna catch a strategic ressource with a city, but that's against the rule) .
As already mentioned: Settle a City 1 tile away from the coast (you won't be able to build a lighthouse then, making all coastal tiles worthless)
Wait for Border pop-up if you are not creative and don't have Stonehenge and play Marathon
Settle a city too close to a creative neighbour -.-