I'd suggest that you use Slavery if its working wonders for you. The other micromanagement stuff suggested in this thread could be a bit much to chew for a beginner. You will need to know how to micromanage eventually though, so you probably should try to take notes anyway.
As you're just starting to come to grips with the game, you could probably just let things self adjust with time. I mean, the only thing all those unhappy citizens do is eat up

and thus halt city growth. You don't actually need to get rid of them - and if you manage to get more happy citizens in, all the better. (Back to work with those Teamsters! Strike is over!) And if you end up with starvation - that will just cut back on city size and get rid of unhappy citizens - that aren't doing anything for you in the first place. It doesn't have to be that much of a problem, really.
Also, you might wanna start looking into optimizing you cities when those red faces turn up. This practically means that you don't need that much

anymore, and can safely switch production to other tiles instead. Since you have a unhappiness "problem" you don't need to worry about a little starvation either.
Experiment and you will eventually get the hang of it. (You do know how to change what tiles a city is working, right? If you don't, you should have played the tutorial...)
edit: It is good to know about the Avoid Growth button, but that is a bit dangerous to actually use, because you will just forget to disable it later!