There are lots of ways to view and/or subscribe to calendars. Depending on your device, it's capabilities, and it's security settings - one way may work better for you than others.
Logging into your Google account and subscribing to the Transit Calendar from your Google account is the easiest. Google will keep the transit data separate from your other appointments, but allow you to see them all at once if you want to.
1) Login to your Gmail or Google Account. https://myaccount.google.com/
2) After logging in, go to https://calendar.google.com
In the left side bar, towards the bottom, there's a section called "Other calendars" with a + (plus) sign next to it.
Click the plus (+) icon.
Choose "Subscribe to Calendar" from what pops up.
Then paste the calendar id of the calendar you want to subscribe to.
Each calendar on this site has the "id" below the calendar.
Here's the Google instructions page:
https://support.google.com/calendar/answer/37095?hl=en
Once you get a few different calendars set up you can watch this video on how to see them all at once (it's for Android but similar to iPhone):