When you set up an email account in Settings - Mail, Contacts, Calendars, you are given the option to add a calendar as well. You can choose your default calendar in Settings - Mail, Contacts, Calendar - Calendars, as well as some other settings.
When you open your Calendar app, and you use an account that already has events, you'll see them there.
At the bottom, in the middle, you'll see "Calendar". Tap it to see which calendars arr available for the app. The check marked ones are visible in the app. Those that aren't, are hidden. You can change visible or hidden calendars by tapping to check mark, or if already so, tapping to undo it.
You can choose how to view the calendar (top): day, week, month and year view are possible.
To add an event, you can either tap the + in the upper right corner, or tap and hold on a day, until you're given the possibility to create an event.
If you use an iCloud calendar, you can choose the colour with which it's displayed. Tap the i in the circle next to it:
This is what you'll see.