Edited to add: The Duomo combo ticket you get online is the actual ticket. It contains a barcode to use at the turnstile at each Duomo site and a separate barcode for the Dome climb. You have to print these tickets, especially the barcode, on paper. They don't work using a smartphone or Ipad/Tablet, as it says on the booking website.
The general recommendation on Tripadvisor is to purchase the Duomo combo ticket online in advance if you want to climb the Dome/Cupola, regardless of whether or not you are getting the Firenze Card.
If you check the booking website at the moment the Dome climb is sold out for the next two days and has only one time slot available on the third day from now. It is usually sold out like this for almost 3 days ahead. In spite of this, somebody on Tripadvisor recently said that, while this was the case online, there were, nevertheless, Dome climb places available on the ticket machine in Florence. But, if you really don't want to miss doing the Dome climb it is better to purchase the combo ticket online.
You have 30 days, from the date you select on the calendar when booking, to start using the Duomo combo ticket. The 72 hours use of the ticket starts with the first Duomo site you enter.
This was changed earlier this year from 6 days and 48 hours.
If you have the Firenze Card and use it to get the Duomo combo ticket, then this is the first use of the Firenze Card's 72 hours. You then have 30 days to start using the Duomo combo ticket. But, there is a risk of losing out on the Dome climb within your time-frame.
FOR INFO: The following is a popup message that appears on the Firenze Card website the first time you access it.
"THE ACCESS TO CUPOLA IS NOT GUARANTEED AND THE RESERVATION IS COMPULSORY
You have to collect the free ticket at the museum ticket office in Piazza San Giovanni,7; after that,you have to make your reservation on the dedicated screen.
PLEASE NOTE that the collection of the free ticket is considered to be 'first entrance': the Firenzecard validity of 72h will start running out since then.
Temporary suspension of access priority to Campanile di Giotto, Battistero di S.Giovanni, Cripta di Santa Reparata and Museo dell'Opera del Duomo."
