There are many ways to start.
If you are the kind of person who wants to write the code yourself, Google is a great resource. Your homepage should be saved as index.html and be included in you share/public_html folder on the department systems.
Other options are available. Use a service paid or not such as Google sites to build your website.
Once you have a website, email the tech people in the department and kindly ask them to add a link to the department website.