You can take something or somebody away if you physically remove that thing from its present location. It is also used when you want to stop or remove something abstract, like an emotion or a physical or mental state.
Ex: Once we were in compliance with the way they wanted us to bag up our recycling, the recycling truck took away our bottles and cans.
Ex: Jane wished that she could take away Melvin's sorrow, because she could hardly stand seeing him suffer so much.
When you buy food and take it elsewhere to eat, you can say you have bought a takeaway. Observe that this noun should be written altogether.
Ex: I'm really not in the mood to cook, so I was thinking we should have a chicken vindaloo takeaway tonight, because I want something spicy!
When you are subtracting, you are also taking away. When you are making something less positive or harming something, you are taking away from it.
Ex: A few dishonest politicians can't take away from the effectiveness of the government, as most of the people who work there are very honest.
Ex: Three or four sloppy plays didn't take away from the team's victory – they played a marvelous game tonight, and should be commended for it.
If you overwhelm someone with beauty or if you surprise someone in a good way, you can say that you have taken their breath away.
Ex: When I first saw my bride in her wedding dress, it took my breath away, because she looked really beautiful.
Ex: The sheer beauty of the Lake District took my breath away, and I couldn't think of anything to say about it.