1. Search for your Contact open their Contact Card
2. Click the Add a Task icon 
3. Select Create a Single Task
If you select View Tasks for this Contact. You can view/edit tasks related to the contact and filter by complete and incomplete. Depending on your permission levels you may also be able to Delete tasks.
See also...
How to attach a file to a task
How to view applied activity schedules
How do I sync my contacts, tasks and meetings to my smart phone and/or Outlook?