There are a few different ways that you can cut out a background in Photoshop. One way is to use the pen tool to trace around the object that you want to keep, and then use the layer mask tool to remove the background. Another way is to use the quick selection tool to select the object, and then use the refine edge tool to fine-tune the selection.
Once you have made your selection, you can either delete the background layer, or you can add a new layer underneath the object and fill it with a solid color. If you want to keep the original background image, you can simply deselect the object.