Outlook has a neat feature called Contact Linking that allows you to link a contact with any appointment, task, other contacts, or even email. Prior to Outlook 2007, the forms had a field with a Contacts button. In Outlook 2007 and Outlook 2010 you needed to go into Contact Options and enable a setting to see the Contact Linking field. In Outlook 2013, this option is gone. You can still link Contacts in File, Properties (or Options dialog) of an open item but that is an extra step.
If you are looking for information about the new Linked Contacts feature, see Outlook 2013's Linked Contacts
Fortunately, there is a way to enable the Contact Linking field: edit the registry.
Type Windows key + R to open the Run command then type regedit and press Enter.
Browse to the preferences key, right click on it and choose New > DWORD. Type or paste showcontactfieldobsolete and set the value to 1 to show the Contact linking field. Set it to 0 or delete the DWORD or to turn it off.
Outlook user key
HKEY_CURRENT_USER\Software\Microsoft\office\15.0\outlook\preferences DWORD: showcontactfieldobsolete Value = 1
Group Policy key
HKEY_CURRENT_USER\Software\Policies\Microsoft\office\15.0\outlook\preferences DWORD: showcontactfieldobsolete Value = 1
Do It For Me
If you don't want to edit the registry yourself, I have a ready-to-use reg file available for download.
To use the reg key, download the file then double click to run it. Answer the prompts to add it to the registry. Restart Outlook for the change to take effect.
(Either file will work for home or SOHO users; the group policy key is generally used in corporations.)