In order to setup your personal homepage with the faculty you need to create the directory public_html in your users home directory (which will be at /users/USERNAME in Linux and at U: in Windows). After that you can put your web content files into this directory.
mkdir -p ~/public_html; touch ~/public_html/index.html
executed in Linux will create the directory and create a file named
index.html in it. This file will be displayed when you point your browser to www.mat.univie.ac.at/~USERNAME. For HTML specifics you should consult w3schools. There you can find out how to design a website.
In order to write HTML it is advised to use a HTML-Editor. Some suggestions can be found at w3schools-HTML-editors.
If you want to design your homepage in a style similar to the faculty homepage, you can use our template. The HTML template contains various places with the word TODO where you have to insert your content.