The super user (or administrator) usually is called root and has a user id of 0. You can check that by entering id root. This will show information about a user called root.
In order to become a super user, you can simply log on using the user root, if it is allowed. So where ever you initially are asked for a login and password, enter root and its password.
Usually, however, root login is disabled. In this case, a user uses sudo to run a program as root. sudo bash will open a root shell (bash) for you. But this only works if you are allowed to use sudo. Usually, this is the case if you are in the sudo group.
You can check the groups you are member of by simply using id, or id your-username.
How the prompt looks like totally depends on the user settings in .bashrc. By default, $ is an ordinary user and # an administrator.