Logging In
To initially create an account, go to arcgis.com and click Sign In. Then, type trincoll in the space where it asks for your organization’s url. The full url should read trincoll.maps.arcgis.com.

On the next screen, select the Trinity College button.

You will then be taken to a regular Trinity College login page where you can enter your Trinity username and password. NOTE: You should need to use Microsoft Authenticator (because you should have that set up).
If you have had a previous ArcGIS account with Trinity, your old content will not appear, as this is considered a new account. For information on linking accounts, see this post from ESRI.
If you are using ArcGIS Pro you will also be asked to sign in and can do so using the same method.