Select the People icon from the left-most navigation bar if you are in Mail, Calendar, or Tasks - OR - if you are in another application, go to the top of the page, select the App launcher , and then select People.

Edit a contact:
 
Find and select the contact that you want to edit. You can only edit contacts in the folders under Your Contacts. When you select a contact, you’ll see their details in the reading pane. To edit their information, select More actions (three dots) in the upper right and click Edit contact. Make any changes that you want, and then select Save to save your changes or Discard to cancel.