With Slice Tool, you can drag over any part of your design and mark that part as a slice. Then you can just double-click the slice area or press CTRL + S (CMD + S on OSX) to open the Export window.
You can even resize or move these slices. While you're moving the slice area, the export preview can be seen in the top right corner in the preview box.
The dimensions of your slice area are displayed in the bottom left corner.
If some layer is blocking what you want to slice, you can simply hide it in the Layer panel on the left.
To delete a created slice (get rid of the selection over your design), just click on the selection area and hit your DELETE/BACKSPACE key.