Right-click on the layer you want to make transparent (if you opened a PNG or whatever straight up it'll be the only layer). On the right-click menu there should be "Add Alpha Channel", if it isn't greyed out (meaning that it already has an alpha channel) click on that.
Click on the Select by Colour tool (or Shift+O) and go to Tool Options to set the threshold to 0. Then click on the sheet's background to select all of the background (a properly made sprite sheet shouldn't have any other content with the same colour as the background). Tap delete on your keyboard and you should have a transparent background.
Click on the Select by Colour tool (or Shift+O) and go to Tool Options to set the threshold to 0. Then click on the sheet's background to select all of the background (a properly made sprite sheet shouldn't have any other content with the same colour as the background). Tap delete on your keyboard and you should have a transparent background.