To search for applications in discover type in the box that says search and then press enter.To install an application after searching press the install button and then enter your password to make sure you want to install it.
You can also browse through different cattegories on the left clicking ont he different categories of applications. If you have any updates you need to do check on the bottom of the left column for updates. If none are available you can click the button to check for updates manually. If you wait and then have updates press apply all updates and then enter your password in.
To remove a package you can look through all of your installed packages you can search in the upper left hand corner and the press the remove button and enter your password to remove packages.