This method of rendering is similar to the Filter > Extract method, only a little different, and in some cases may turn out to be easier. Get your image that you want to cut out..and select the Brush Tool.. While the Brush Tool is selected, select this icon to enter Quick Mask Mode.

Reset your colors to default by pressing D on your keyboard, and start tracing around the outline of your image. You should see a transparent red line appear over your image as you outline.

If you make a mistake while doing this, simply press X on your keyboard and go over the place again with your Brush Tool. Remember to press D to carry on to the next step if you do this. OK so now you should have the main outlines done. Select the Paint Bucket Tool and click in the image you just outlined. It should all turn red.

As shown before, press X and make it a nice tight fit around your image. Zoom in and slowly erase the lines if you need to. Now go back to Standard Mode (press the icon next to the Quick Mask Mode button you clicked up the top). You should have a line of 'marching ants' walking around your image now.

Now, simply tap Delete and your background should be gone!