When you get an egg, by exploring, it goes automatically in your hatchery. From there, you can incubate them. It is always best to wait until they are fully incubated (100%) to hatch them. If you hatch at let's say 80%, they have a higher chance of failing. Even if the egg is fully incubated, it still has a little percentage chance of failing also, but that's just part of the game.
If you have any further questions, feel free to ask.