To update your website, you will need an FTP program. There are several great free programs available online, such as CuteFTP and WS ETP. If you already have an FTP program, you simply FTP into your account and upload your new or updated html files.
It's also possible to upload your files using FTP via your browser. Simply type the following address into your browser and it will ask you for the login info: ftp://ftp.yourdomain.com/yourdomain.com. Enter your login details and you're ready to upload!