I'm going to take a guess that you don't really know much about specialists in general, if this isn't true you can ignore this.
I took an example city and some screenshots to show how specialists work.
Here's a city in your empire (hypothetically):
As you can see, it has a population of 7 and is working the 7 tiles outlined in white. Your citizens in the city are being automated currently. Now some of these tiles are unimproved, so you aren't getting much from them yet.
You may want to de-select these tiles in favor of running specialists with some of your population.
If you click on the tiles you don't want to work, it pops up citizen specialists on the right hand side of your city screen.
In this screenshot, I've taken 2 of your citizens off of the unimproved grassland tiles and turned them in to citizen specialists, which give +1 hammer to your city, each. You can see these guys in their white hats and shirts.
Now you have these 2 citizen specialists, but they're not doing much good at 1 hammer each. Instead you may want to instead turn them in to another kind of specialist.
You can do this by clicking the [+] symbol next to another kind of specialist above the citizen specialists. Each time you click the [+] symbol on another kind of specialist, it will remove a citizen specialist and turn him in to the specialist you have chosen. If you press it more than 2 times in this case, it will also start removing citizens from the worked tiles in your city and turning them in to that specialist as well.
In this screenshot you can see I've turned the 2 regular citizen specialists in to scientist specialists.
These scientists give you extra research as well as great scientist points, which will eventually generate a great person (always a scientist unless you have other factors adding great person points in this city, such as a world or natural wonder).
You can run more specialists if you have the buildings to do so (library allows the 2 scientists very early in the game), or if you're in the caste system civic, which allows you to turn as many citizens as you want in to merchants, scientists, and artists. Just remember that your specialists need 2 food each just like any other citizen, so if you select 2 scientists you are losing 4 food, which could starve your city if you don't have a surplus.
As you can see in my example, the city growth goes to "stagnant" because I had exactly 4 extra food, just enough to work 2 specialists without starving.
Hope this helps in some way