To install ArcGIS Pro on your Windows PC:
Be sure to install the DOT NET runtime before trying to install ArcGIS Pro.  The installation file is found at the root of the shared ArcGIS folder.

Next, navigate into the 3_7 folder and  download the ArcGISPro_37_199633.exe
Install this software and you will be set for the semester.
 
There will be updates patches as well, and you can install these directly from your own computer without needing to use the server again.

NOTE: Your instructor may require you to install additional ArcGIS software, but the base installation is taken care of with the steps described above.