Not really sharing the contact by Outlook's terminology but, practically speaking, another person can access that contact or contact group and add it to their Outlook by using the 'Forward Contact' function.
Forwarding a Contact Group
1. Go to 'People' (formerly 'Contacts') from the navigation pane.
2. Select the desired contact or contact group. A contact group is shown in the example below by the adjacent People icon.
Adding the Contact or Contact Group in Outlook - actions for the recipient
1. The recipient will receive an email with an attachment.
2. Now for a bit of juggling:
a. Open the email in its own window. Here you can see the forwarded contact as the attachment "AlphaSys".
b. Go to 'People' (formerly 'Contacts') from the navigation pane.
c. Bring the email window you opened in Step a. to the front, then drag-and-drop the attachment into 'Contacts'.
d. The entry has been added to your contacts.