When you click on the Leaves menu option, you are taken to a monthly calendar that will show you your current leave requests. Naturally, if there were no prior leave requests made, or there are none for the current month, then the calendar is empty.

Click on a day in the calendar to tell Odoo to schedule a leave request beginning on that day:

In this example, we have requested a Sick Day. It's possible to configure leave types to only allow a specific number of days or a specific length of time. The Personal Days leave type, for example, is configured this way by default in Odoo.