I have entered a contact in Civi. I want to reminder myself to contact her in a year. I don't have administer privileges. I can't find anything within the contact to let me do this.
You can create a scheduled Activity with this contact. https://docs.civicrm.org/user/en/latest/organising-your-data/activities/ via the Actions button on the contacts Summary screen
If you add the dashlet for activities to your dashboard, you will also be reminded of this whenever you log in until you mark the activity as completed.
If your administrator isn't willing to set up the scheduled reminders, then you could always just put a regular calendar reminder in your regular calendar.