Use the Select rectangle (S), Select ellipse (A), Lasso (O), Wand (W) and Select with pencil (I) tools to select a region of the image.
After you are done with selecting a region of the image, switch to the Transform (F) tool to move, resize or rotate it. The outline of the selection will change from black-and-white (editable selection) to blue-and-white (floating selection), and only the bounding box will be shown.
If the Transform tool is already active and the selection is still editable (i.e. its outline is black-and-white), switch to any other tool and back.
After activating the Transform (F) tool, you can:
In short, you can do perspective transformation by pressing Shift.
You can fine-tune the position and aspect of the floating selection with Edit | Transform | Transform selection. Here you can enter exact numeric values.
You can merge the floating selection with the layer below by pressing Esc or Ctrl+D, or by choosing Edit | Deselect All.
Note that the floating selection acts like a layer meaning that it shows up in the layer list as a separate entity. Here you can drag this "pseudo-layer" around to position the floating selection over a different layer.
You can delete, cut, copy and paste the selection as you normally would, with the Del, Ctrl+X, Ctrl+C and Ctrl+V keys.
Edit | Paste as New Page (Ctrl+Shift+V) and Edit | Paste as New Document (Ctrl+Shift+D) are also useful.