take off clothes, glasses etc. means remove something (e.g. It was warm, so I took off my jacket)
take off means leave the ground (for planes) (e.g. After a long delay the plane finally took off)
take something out means remove from a place (e.g. Can you take the garbage out to the street for me?
take somebody out means pay for somebody to go somewhere with you (e.g. My grandparents took us out for dinner and a movie.)
take up a hobby, a spot, an activity etc. means start doing it (e.g. Ann took up photography a few years ago. She takes really good pictures)
take up space or time means use space or time (e.g. Most of the space in the room was taken up by a large table)