To edit and update your homepage go to Entries > Singles and then click the Home entry. Here you will see various fields for your homepage carousel, intro copy, and sidebar.
The first fields you will see are for the carousel. Each slide allows you to add an image, which will be resized to 940px * 400px automatically. Optionally you can also add a caption. There is a limit of 3 slides. Slides can be reordered by grabbing the handle on the right and moving up and down. Additionally you can disable or delete a slide. Disabling a slide keeps the content in the entry but it becomes hidden on the front end of the website.
When there are fewer than three slides at the bottom there will be an option to add an additional slide.
At the bottom of the homepage are two square images that link off to internal pages. This is powered by the field called sidebar links. In this field you can select a link (internal or external) and the color of the title bar for the square.
When adding an internal link, by default the title text will be the title of that page. You can override this by adding text where it says Link Text.