Be sure to make a backup copy of the original image (or save it under a different name and then proceed with modifications).
To remove the background first method, select the snipping tool. They circle along the contour of the object around which you want to remove the background. Closing the loop, adjust the position of its points, and optionally add a new, intermediate position which is also correct. Then hit the middle of the object, and the path becomes solid, and the points will disappear.
Copy a selected object by pressing Ctrl+C. Create a new image of a size such that the object he had placed. Select the desired color of the background. Paste the clipboard contents by pressing Ctrl+V. Select the instrument "Rectangular selection" and click on any point outside the contour. Then save the result under this name, which is still there. Similarly, you can paste the clipboard contents into the existing picture with the background. Do not forget to deselect move object with the arrow keys to the desired location.
You can do without creating a new image. To do this, click "edit" then click "Invert selection". The object will no longer be highlighted, but so will the background. To remove it, the old version of GIMP, press Ctrl+K new - Ctrl+X. After this select the desired color of the background and do the "Image" - "flatten image".
Removal of the background by the second method instead of the snipping tool use the Eraser tool. Select the desired color of the background, and then set the diameter of the eraser to be easy to erase the background around the object. Clearing the space around him, the remaining sections of background remove using the tool "Rectangular selection" and the key combination Ctrl - +K (or Ctrl+X). Slide image as described above.
Now, to move the object to another background, select the tool "Magic wand" and click anywhere in the background around the object. Then make an operation "Selection" - "Invert selection". Press Ctrl+C. Open the file with a different background, insert the object by pressing Ctrl+V, turn the instrument "Rectangular selection", correct the position of the object with the arrow keys, and then tap anywhere on the background. Save the result under a different name.