Now there are alot of ways to get rid of the background and you have to pick and try out each one to find out which one or combination works for you.
First of all it is a good idea to start out with a transparent background. This is done when you make a new document in PS.
File > New ...
Then under Background contents scroll down to "Transparent" > click, OK.
Now you have a transparent background that you can work with.
(this is what a transparent background looks like)
If you are working on a certain picture or cartoon or render one of the basic tools you can use is the eraser tool. When you start out with a transparent background then any areas that you use the eraser on your picture are now transparent. If you practice with the eraser alot then eventually it will be really easy and you can use more advanced cutting tools with confidence.
(Using eraser tool)
Now in order to keep your image with the transparent background you have to save it as a .png
File > Save as ...
Then in the format bar scroll down to .PNG then click save.
Then when you upload the image to the internet it will not have the background and it will take the color of the background on the site.
Oh and one more thing. Don't forget to save it also as a Photoshop image (*PSD;*PDD) so you can keep all your layers. Once you save it as anything else like PNG or Jpeg or GIF, and exit Photoshop the layers merge to one and you can't recover the layers used previously.
(+reps for tutorials are always appreciated
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