Crop out unselected areas with the Crop Selected layer. First make a selection with the Selection Tools, then click the Crop Selected button in the tabbed toolbar. This will remove unselected pixels and resize the image to match the bounds of your selection.
Use the Smooth/Sharp slider to smooth the edges of your selection.
You can go back and change the cropped area by clicking the Edit Crop Selection button. Use the selection tools to change the selected area. When you are satisfied with your new selection, click Apply to re-crop to the new selection.