In order to remove an element within one photo and place it into another image, you need to know about:
1) Making a selection - This can be done in numerous ways within Photoshop or GIMP. You would not use Lightroom to do this since it does not have the ability to select and copy data from one image and place into another.
2) Transform or Free Transform - When you place an element into another image, often you will need to change the size of the new element so that it's in proportion with everything else in the image. You do this with the "Free Transform" tool in Photoshop. I'm sure GIMP has a similar tool, too.
3) Working with layers - When you place an element from one image onto another, you will automatically create a new layer. This is true in Photoshop. This allows you to edit the new element without affecting any other part of the image.
4) After you've copied, pasted and transformed the new element, you will need to adjust its contrast, brightness and color to match that of the main image. Unless you get the new piece to have the same color temperature, brightness and contrast (not to mention that the type of lighting and direction must be equal, too), then the image will look obviously fake.