Well, it depends on how complex both of the pics are.
The easy way to explain it and for you to quickly try it is by using your Lasso Tool, and try to outline the pic of the bird - this basically selects a portion of your image. Then, while it is selected, you need to select your Move Tool (at the top of the toolbar), and drag that selected area into the photo of the dog. It will automatically add a new layer in the dog photo, and you can use the move tool to place it precisely.
Of course, you will see that the Lasso tool does not allow you to cleanly select JUST the bird - you will also select some of the background. You can either use your erase tool and start erasing the unwanted background around the bird, or you can try again and start tracing the bird with your Pen tool. I don't know how fluent you are with photoshop, so I tried to explain this as simply as possible.
Good luck!
