There are many ways to create entries in Day One. The screen shots are mostly from iPhone, but they apply to the iPad as well.
Tap the Camera icon to open the photo picker/camera option to start an entry with a photo. The album can be changed by tapping the album name at the top. Tap the camera icons at the bottom left to open the in-app camera to take a photo or video. There are zoom controls at the bottom right to see thumbnails a bit larger.
Tap the Microphone to begin recording an audio entry. Long press the microphone for one-time recording options, including Browse to locate audio in the Files app. The default setting for audio recording can be adjusted in Settings > Advanced > Transcribe to Text.
Tap the Paper/Pencil icon to create a blank entry. Media can be added later in a blank entry. See here.
Tap the + icon at the bottom of the screen to access additional options, including Today, Templates, etc.
When you are in Calendar view, tap a date to open the Today view for a variety of options to create new entries. Today replaces the Activity Feed view. Long press a date in the Calendar for a menu.
Long press a location in the Map view to create a new entry at a specific location