Using a university HPC cluster is very installation dependent. Did they install ANSYS Remote Solve Manager (RSM)? That makes it almost trivial to use the cluster from ANSYS Workbench on a workstation on the university network. If they did not install ANSYS RSM then you have to do more work. You can write out the input file from Mechanical, then move that input file to your home directory on the university cluster.
Is the cluster running Linux or Windows? You need to know the command to submit a job to the cluster. You need to know the command line to start the ANSYS solver. One of the parameters on that command line is -np 8 where 8 is the number of processors (cores) you are requesting to use during the solution. You might request more than 8 but more may not be any faster and may even be slower and is using up resources that others could use.
What version of ANSYS are they running on the cluster? Do you have the same version of ANSYS on the computer with the student license? That is a requirement.
On your student license is the full ANSYS Help system. There is a lot of information on HPC there.