When I booked my tickets on Online Travel Agencies I get the message on the itinerary that this is an itinerary only and that it can take up to 24 hours for a ticket# to be issued. I will call up the airline to see that they have a Confirmation# and that the itinerary is the same as I booked on the online travel agency's website. Then I call up the Online Agency to confirm that my payment information has been processed and have them e-mail me the E-Ticket with Ticket#.
After I get the Ticket I will then call the airline again to confirm that the TIcket# is the same and then add my Frequent Flier miles, Seat Preferences Meal Requests, Known Traveler Number Etc.
So it helps to confirm the same details with the airline. I am very OCD when it comes to booking and confirming that the vendor has the same details rather than to show up at the airport without a reservation or an issued ticket. I will then add my ticket to my Airline Online Profile and check for any schedule changes and call the travel agent to change flights if needed.