after I have assigned a citizen to work it tells me now that my citiy is stagnent for growth and none of my cottages are becoming hamlets?
The first business with a new city is to establish its food supply, so you almost always want to settle a city near special food resources--crops, animals or seafood.
Then you need two things to exploit that food--a technology and a tile improvement.
Technologies: Agriculture for farming crops, Animal Husbandry for pasturing animals, and Fishing to work seafood.
Improvements: you need a Worker or Workboat to build these, so an early [often first] build in a new city is one of those. When it's built, send the Workboat to the seafood tile and deploy it; similarly, send the Worker to the land tile and assign him to build a Farm or Pasture.
Developed food tiles will give you 4-6 food, which is a nice basis for the city population to grow. The key point for this is that each citizen consumes 2 food.
Re Cottages > Hamlets, usually you should build Cottages only on tiles which have 2 or 3 food, ie grassland or flood plains. That food means the tile is self-sustaining, ie it supplies enough food for the citizen working it. It takes 10 turns for a Cottage to become a Hamlet, and another 20 turns for that Hamlet to become a Village, then 40 more turns to become a Town.
Why this matters is that you'll want some citizens to work tiles which have 0-1 food, typically mines on hills for production. So those guys are costing your city 1 or 2 food, which you make up from your farmed rice or pastured pigs etc.
Mess around with it and it'll click with you after a while
