Hi! I've played 3 games now and not even once have I pleased an angry population... it was always (mostly) because the city was too crowded. How do I give them the space they want?
Also, most of the time there has been sick people: they were sick from "Flood Plains" (or something like that)... how do I solve this problem?
You can get extra happy faces from getting resources like fur, wine, etc. Also, some buildings - like theaters and coliseums, help. Some civics - like hereditary rule or Representation or free religion, can increase your happiness. Heredity rule, for example, gives you more happiness the more military units you have in a city. Also, happiness comes from temple buildings, so the more religions and temples you have in your city the happier your people are.
Sick people're harder to deal with. Some resources, like sea food and deer, give health. Some buildings like aquaducts give you health. Some terrains - like you said, flood plains - are just disease ridden evilnesses that make your population sick. Forests inside your city radius also give health. Health is harder to get up then happiness, but at least sick people only require extra food. Angry people don't work at all!
You can certainly use slavery and whipping to keep your population down in the early game, below the point where there're too many angry faces. In fact, a really powerful tactic is to make a lot of farms around your cities so they grow fast, and whip them to death to get your buildings and units out really fast in the early game.
Also, specific leader traits.. like expansive (+2 health in all cities) and charismatic (+1 happy) work in your favor. There're wonders that work wonders, too! But I don't think I could list all the things you can do - the important thing to do if you don't have the manual is just spend a lot of time browsing through the in-game help. The civilopedia is not only helpful, it's interesting and fun to read! Read what's under your mouse; you'll get a feel for it all eventually.