Discover allows you to search for applications by using the search box. Clicking on a program will give you a description of it. When installing or removing software, you will be prompted for your password. You can also browse through different categories on the left clicking on the different categories.
Discover allows you to update software using the Updates tab located on the bottom of the left column. You can click the button to "check for updates" manually.
To remove software use the Installed tab. You can browse your installed packages, search using the search bar (upper left corner), and the click the remove button to remove software.