There are several ways to remove backgronds from images, this is just the way that I prefer.
In this tutorial you will be using the Mask tool located at the bottom of the layers pannel, its the one highlighted in the red below.
You also need your trusted paint tool (). We are going to use a very simple image just for the purpose of this tutorial, you can download it here or just pick an image of your own to use.
Open the image and click on the mask tool, in the layer pannel a white canvas will appear next the the thumbnail of the plane image.
Click on the white canvas and select your brush tool, with black as the selcted color. Now it is simple a matter or drawing on the section want to make disappear. You can actually use the lasso and paint bucket tool in the same mannor as the brush tool.
Now here is the beauty of the masking tool, in the image below I have seem to have erased part of the image as well as some of the background.
Because we have been using the masking tool instead of just deleting/erasing the background, the whole image is still intact just hidden from view. Switch your foreground colour to white and paint over the section you want to bring back. and volia its back!
Finish cutting out the rest of your object and you have finished.
Because the mask tool never really gets rid of the background just hides it, it does mean that you can use a wider range or tools to blend the image into the background, great if you are working with flilmsy details like hair. You can use the smudge to blend the mask layer, you can blur it, you can fade the brush tool to any opacity. Experiment as see what you can do with it.