To view an existing contact, simply navigate to the folder where the contact is saved in (or search for the contact) and then click on the contact's name.
To create a contact, you can:
click on New email / New contact in the left menu - this will create a contact in the root contact folder
or
open the contact folder that you want to create the contact in, and click New contact
To edit an existing contact, simply navigate to the folder where the contact is saved in (or search for the contact) and then click on the link corresponding to the contact. If this link is not present, you are not authorized to edit contacts in this folder. After you have input or changed the contact details, click on the Save button.
Tip: from the contact folder, click on the contact's email address to open a new email addressed to the contact. You can then normally type your message and send the email.