You can invite someone to a card when you create the card, or after it has been created.
While creating a card, click "+ Invitees" and choose other people from your workspace to share the card with. This will cause the card to show up in their Watching feed. You can designate whether the person has edit or view privileges.
Please note that people with view permission on cards can add comments on the card as well.
Click the Share button in the top right corner of the card view to open the Share window, and choose people to invite. You can also remove access from people through the Share window.