Grammar is all around us. If you are learning about past simple, then don't just look at the example in the textbook, or what your teacher has given you, keep looking for more in the world around you. When you are on the train or tram look at the advertisements. When you are watching a TV series (with subtitles) then try to look out for the grammar.
Once you have learnt a new grammar point, then usually the way people use it will become more obvious. Before you paid attention to that part of the language, you probably didn't notice it as clearly when people use it.
If someone tells you that somebody's hair is starting to go grey, the next time you see them you will look very closely to see if it is really true. Then you can see it clearly, he really is starting to go grey. But if nobody told you about that, you wouldn't have noticed. Language is the same. When we focus on a grammar point it essentially highlights it, it becomes easier to perceive.
After taking language classes and hearing the teacher talk about the grammar, and then doing the exercises and the speaking activities, the language often still feels quite unnatural, and you might not be sure if it is really used like that.