Set up Birthdays

Open Birthdays in the dashboard and turn on the switch at the top right of the panel. It saves at once.
Set the server's timezone under Settings > Locale & Timezone if you have not yet. The announcement hour is read in that timezone, and it is the fallback for members who have not set their own. Without one, UTC is used.
On the Settings tab, pick the Announcement Channel. Leave it at Disabled to celebrate with the role only.
Pick the Announcement Hour (default 9 AM).
Choose the Announcement Mode: Individual posts one message per member, Bulk posts one digest a day. See Announcements.
Optional: pick a Birthday Role that members hold for their birthday.
Optional: turn on Require Birth Year if you plan to use age roles.
Click Save Changes in the bar at the bottom of the page.
Tell members to run /birthday set with the day and month as numbers, for example /birthday set day:15 month:3 for 15 March.

Settings in individual mode — Individual mode: one announcement per member

Note

The bot needs Send Messages in the announcement channel. For the birthday role and age roles it needs Manage Roles, and its highest role must be above those roles.

Where members save their birthday

/birthday set in any server with Birthdays turned on. The first time, members without a timezone are asked to use the server's timezone or set their own on the website.
The Birthday section of the dashboard's account Settings page, which also holds their timezone and the leap day choice.
A form with a birthday question, if your server uses Forms.

A birthday is saved once per member and used in every server with this bot.