Ok, so I downloaded and uploaded this program "joom gallery" successfully and is added under components. However, now is where I am stuck. I have a "photos" page already made with joomla article and would like this program to be set up on that article page. How can I make this possible from here? I am stuck any help would be appreciated!
You can use a number of plugins to embed components or modules within an article. See here: http://extensions.joomla.org/extensions/core-enhancements/embed-a-include
I would recommend you pick the component that best suits your needs and click on the documentation link - if the extension developer has produced a guide you'll pick it up.
For a simple but cool gallery I recommend using YooGallery. Upload images to an asigned folder with the filenames named as you want the captions to read and you are done.