WordPress versions are being updated and so with how to delete a theme. In the older versions the delete button is visible after a theme is deactivated but with the WP v3.8.1 it is done differently.
If you want to delete a theme you are currently using, first you need to activate a different theme and then click on the image of the theme you want to delete.
Doing that will show you the delete button on the far right bottom of the page.
Click the delete button and a pop-up window will open that asks you if you want to delete the theme. Click the OK button if you are sure to go.
After hitting the OK button you will see a note that your theme is now deleted. You can now upload your updated theme.