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Haha the other day someone I know used their last 12 PokeBalls on a Pokemon and didn't catch it. What a fail. But yeah, you just click on an egg and there should be an icon that says Start Incubation, then you can choose one of your incubators to put it in. Using a Razz Berry before throwing a PokeBall can definitely help on some of the higher level ones.
Here's what comes in the eggs in case anyone didn't know:
Here's what comes in the eggs in case anyone didn't know: