When you first start using Microsoft OneNote for iPhone or iPad, you'll be prompted to sign in. After you've signed in, your notes will be synced across all of your devices.
In OneNote, tap Sign in.
On the Sign in page, type the email address or phone number that you'd like to use to sign in, and then tap Next.
Type your Microsoft Account and password, and then tap Sign in.
Note: Your Microsoft Account is an email address used to sign in to Microsoft services. You have a Microsoft Account if you have any of the following: Hotmail, Outlook.com, Xbox LIVE, MSN, Messenger, OneDrive, an Office 365 for home subscription, a non-subscription version of Office 2016 or Office 2013, or your own email address that is registered as a Microsoft Account (Gmail, Yahoo, or others).