From the "Edit Page Dialog" first, ensure you are using a layout that supports a picture. You will see the "Picture" tab.
Having clicked on the Picture tab, click on the "Upload" button under the "My Photos" tab to open an explorer window for you to choose your files. You will need to navigate to the location on your computer to locate your photo.
Having located your photo, click on it to highlight it and then click on the "Open" button. Your photo will then be uploaded and you will see a progress bar appear. As soon as the photo is done, it will appear under the heading "Uploaded Photos". You can also use the shift button on your keyboard to select multiple photos if you want to upload more than one at a time.
Now that your photo is in available, you can select it for inclusion on the page by clicking on it. An orange border will surround the selected image.