That was their first foreign language. After that, it's all down hill. It wasn't by studying English grammar. Actually, they didn't learn any grammar until they already knew how to speak pretty well. The concept of teaching languages by teaching grammar was developed by linguists.
Linguists are kind of like English teachers, they love grammar.
Unfortunately, as we just discussed, most of us don't learn that way. Think back a minute, to when your children were first learning. They didn't start with sentences, but just sounds. Imitation is the key. What's happening is that they are trying to repeat the sounds that they hear.