You cannot use your frequent flier miles to pay for a ticket purchased on a travel website that is not the airline's own portal. The major travel websites generally are not airline partners but resellers of tickets.
If you want to redeem your frequent flier miles, you must go directly to the airline's website or ticket office.
Expedia
One of the larger online booking sites, Expedia.com, allows you to enter your frequent flier number and accrue miles when you purchase your ticket. However, you cannot pay for your ticket using frequent flier miles.
Priceline
Priceline also does not accept frequent flier miles as payment.
When purchasing tickets with Priceline.com, you can enter your frequent traveler information but they do not guarantee that your miles will be logged with the airline, so it is best to double check before departure.
Orbitz
Like Expedia, Orbitz.com allows you to store your frequent flier details within your account profile, but you cannot use your existing miles to purchase tickets.
Travelocity
Travelocity.com, like many of its competitors, will allow you to store your frequent flier details online so that when you purchase tickets, the miles will be added to your account.
Also like the others, you cannot use frequent flier miles to purchase tickets from Travelocity.
Travel Search Engines
Travel search engines, such as Kayak.com and Sidestep.com, do not sell tickets. Instead, they search travel websites and other sources to find a range of prices for the ticket you wish to purchase.