How do I store a vCard to my Lumia device People (Contacts) after I received a vCard via SMS?

All received contact cards are stored inside the Contacts Share application. Newly received contact cards are highlighted with accent color in the list of all received contact cards.

By tapping on a contact card, a procedure will show up which allows you to add it to the Contacts application. First you can choose to which account the contact card should be assigned to (e.g. Windows Live, Outlook), after which an editor will show up that lets you edit the contact. You can finish adding the contact card by pressing Save.