The Calendar view in Day One indicates the days on which you have entries created and allow you to create new entries, view day summary, or view On This Day entries.
Tap the Calendar icon at the bottom right to access this view.
The current date selection will appear black. The days that have entries will be colored according to your selected journal. Any days that do not have entries will be white. Tap the Calendar icon a second time to scroll back to the current date.
Tap any date to open the Today View.
The Today view shows entries created on that date. These can be hidden or shown by tapping the arrow next to "Entries". This also shows sources for new entries including Photos, Places, Events. Tap these to create new entries using that content.
Long press on any date to get a contextual menu.
To start a new entry, use one of the sources in the Today view or tap the + icon at the top left of Today. You can swipe between dates at the top or simply swipe from left to right.
Tap the Calendar icon at the top to invoke a date selector
On macOS, click the option for Calendar at the top of the app. Click any date to see the entries for that date, plus data from the Today view. Right-click (control+click) on any date to Create New Entry on that date.