This tutorial will take you through the process of removing image backgrounds step-by-step using the freely available gimp software. This tutorial assumes you are running the Windows version, but the concept applies equally to other versions of the gimp and other photo editing software such as Photoshop.
The assumption is that you have a basic understanding of how to use the gimp.
There are many ways to achieve this - the method that we will describe here uses the Fuzzy Select Tool - a fairly quick and precise method that can be mastered easily (the image below took around 15 minutes to remove the background from).
Using the Fuzzy Select Tool select the part of the image that you wish to remove. The aim is to end up with an image which resembles the one below. You should have the "marching ants" around the area of the image that you wish to keep.
This is what you are trying to achieve around the entire outline of the portion of the image that you wish to keep.
Add transparency to the image by using Layer > Transparency >Add Alpha Channel. This makes it easy to add another background layer or paste your selection into another image.
Press the Delete key to remove the selected background. You should be left with your selection on a checked or transparent background.
If you were to save the image at this point you would have an image without the background but with jagged edges.
Grow the slection by 2-3 pixels
This is done from Filters > Blur > Guassian Blur
If you are saving th eimage as a JPG (which you probably would be for display on a website) you will need to select Export when prompted as JPG files don't support transparency. The transparent part of the image will be filled with white.