If you are looking in "Photos" and the "Camera Roll" - just bring up the photo full-screen, and at the top right corner, you'll see an icon of a Garbage Can. Touch that icon, and the image will be deleted from your pad.
To delete that image from your home screen, just go back to the process that you used to put it there in the first place, and replace that home-screen image with a different one. (you might have to do that operation first before deleting the image from the Camera Roll... not sure on that.)
Let us know if you still have trouble or if there's something different about your problem that you didn't elaborate on.
Brian - Sent from my iPad using iPF