SSH
General
Secure Shell (ssh) is a commandline-tool for logging into a different computer over some network (e.g. the internet) and for executing commands on that machine, as if one would be sitting there instead of the own computer. So you use ssh to build a connection to the other computer and can then interact with it, using it's shell. It is commonly used to login to the login nodes of a supercomputer.
Access
OpenSSH is the standard ssh client on Linux and the Mac and it is freely available for everyone.
On Windows, you can use Putty, Bitvise or the GitBash (coming with ssh) which is also free. On Windows 10 since Update 1709, Microsoft has packaged "ssh" right into windows. You can thus open a cmd window (Start - type "cmd" - <ENTER>) and run ssh username@hostname.domain like you would with Linux or MacOS.
Sometimes access to a cluster's login nodes is restricted to certain networks within the university/facility, so you can connect while being on the campus, but not from your network at home or at other institutions. To nevertheless access those login nodes from external, one can 'pretend to be inside the network' by using a Virtual Private Network (VPN) provided by the university operating the cluster.
Usage
Logging in with OpenSSH on a Linux Cluster is done with:
$ ssh -l <login> <cluster>
Here <login> is your username and <cluster> is one of the login nodes of the system, you are trying to connect to. At the first login you will be asked to verify the authenticity of the host. If the shown host is correct, enter yes. After pressing RETURN you will be prompted to enter your password for the provided username.
If you need to start graphical applications you need to enable X11 forwarding/X11 tunneling by your ssh client.
For OpenSSH this is done by giving it the command line option -X (or -Y if the previous did not work):
$ ssh -X -l <login> <cluster>
This might or might not work depending on the your operating system, because it requires an X11-Server running on your local machine, which is not available by default on Mac and Windows. To utilize graphical tools anyway, you might want to look into FastX, which provides the necessary functionality for Mac and Windows.
For more security and ease of use you should consider setting up authentication via ssh keys.