When you decide to follow a user, that user's Instagram photos will appear in your feed, which can be found under the "Feed" icon on the lower menu. You can press "Like" on any photo to let someone know that you admire their photography, or you can leave a comment.
When you take photos using the Instagram app, they will always appear in the feeds of the users who are following you. You can browse through the "Explore" tab to find new users to follow and creative photos to look at.