Summary: If you've received an email with your e-ticket than your flight has, in most cases, been confirmed.
Within a few minutes of payment, you should receive email confirmation of your booking request.
Most bookings are processed immediately. You'll usually receive your e-ticket within 10 minutes. In some cases, like bookings with more complex itineraries, it may take longer. But, you should always have your confirmation in less than 4 hours.
You can also see the status of your reservation in Manage My Booking. At the top right of the page, next to the title of your trip, is a green, yellow, or red indicator that describes your booking status.