How can I change a picture background without dragging the image in the picture?

Use Magic tool to select Background Remove and replace with other backgroundOr better use pen tool to draw a shap around the image you wanna move and Make Selection over the shape under paths tab , and Copy paste it on a new background

Question is not clear actually. If you have already cut image and you want to add background then you have to add one new layer and fill this with any colour or gradiant. "Shift+F5" is the shortcut key for fill colour.