To add members to a board, select "Add Members..." from the board sidebar. Search for a user by name or enter an email address to invite them to the board. Click their name to add them to the board.
You can add members to boards even if they are not already using Trello. Just enter the person's email address and click "Send." The user's permission level will be considered "Virtual" until they join Trello, but you can still add the user to cards.