How do I adjust and shift itinerary dates correctly?

You can go to the title box and click the gear icon and change the dates there. 

Or on the right hand menu (to the right of the bookings) you can click on "Adjust itinerary dates"

Once the new start date is there, on the booking section add your booking to the new date that now shows up.

Please make sure to check the box "Shift all bookings according to new start date, preserving order." This will make sure the bookings move in the right order.

Watch this video to find out how you can successfully switch itinerary dates without changing the order of your bookings.