To start off you will need to open the image that you want to get rid of the background on. To do this you will just need to navigate to File > Open and then just browse to where the image is saved on your hard drive. Once you have the image open you will need to go to the Paths Tool in the Toolbox window it is the that looks like a pen. Now what you will need to do is just click on the border of the image to create a small dot. Then to create a path around the image just click around the image to create a path all the way around. Then once you click back on the first dot it will leave a open space between the last and first dot.
Image with path drawn around it
Now after you have you path around the whole image you will need to go to the Toolbox window and click on the Tool Options tab. You will then need to click on the button that says Selection From Path. This should now make your path into a selection.
Image with a Selection Path around it
Now you just have to press Ctrl + C to copy the selection then press Ctrl + V to paste the image back onto the image that you already have. Now you will have to click on the New Layer button in the Layers tab in the Toolbox window. This will now put your pasted image onto it's own layer. From here you will need to select the background layer and then click on the Delete Layer button. Now you should just have you image with no background.
Image with no background
From here you can be done or you can move on and just copy and paste this image onto another one and resize if needed. If this method does not seem work the greatest for you or if you think that you have a better way on how to do this you can post it in the comments or you can send me an e-mail at firstname.lastname@example.org. This method does seem to work very well for me though in the past and just remember to have fun with it.