Regarding specialization...
This is really just about choosing which of your cities is going to be the BEST at a given task, and then upgrading that city accordingly. A city next to 2 gold mines and a river is a lot more capable of generating science output, so you want to build EVERY science upgrade in that city, and build it there first.
Other cities may eventually get libraries and laboratories but they will get them when it is convenient (no war), rather than as soon as the upgrade is available.
Say you want to build a few libraries. The first city you build one in, is the city on the river with the gold mines. Other cities will be building units to protect you, or barracks, or settlers or workers.
Regarding specialists (Engineers, Artists, Scientists, Priests), you can get a better output from these people than from a cottage, but it requires a set of circumstances. Say you have 70% set to science and you are in a republic with all the relevant techs and civics to give you 7 coins on a town. A town will only put ~5 gold into science (70% of 7 is ~5), whereas a Scientist will put in 6. If you +100% science that will result in a whopping 2 coin difference.
However the town would give you some extra coin for money and food( and perhaps trade), whereas the scientist would give you Super People Points.
So it is a tradeoff. Basically what you want to do is pick a city to develop super people--preferably one that has alot of food to offset the loss of food, and also one that has good science/production/culture multiples.