To book selected items within an itinerary and obtain client approval in Tern, you should create a partial itinerary focusing on specific components, such as hotel stays. The client must log in using a matching email and have a Tern Traveler account. Send the itinerary for approval, and your client can authorize payment for parts of the trip. They can also choose to skip selecting preferences by clicking 'Choose Later'. Email notifications will inform you once the client has approved.