Madrid airport to train station

Have you tried the airport's website?

The Cercanias train , C-1 , goes from the airport to Atocha Station ( departure point for AVE trains to Sevilla ) in about a half hour .

+1 for Steven's suggestion

http://www.renfe.com/viajeros/larga_distancia/servicios/conexionAeropuerto.html

I also recommend steven's suggestion. I landed in Madrid around the same time last month and was to Atocha around 10:00 am. You shouldn't have any trouble catching the noon train. If you land in T1 like I did, just go outside and take the airport shuttle bus to T4 and the train station is in the basement. If you already have your ticket to Sevilla, a transfer from the airport to Atocha on the Cercanias is included.

As Steven and the others have suggested, The Cercanias C-1 train is one of the best ways to transfer from Barajas Airport to Atocha's train station where you will take the train to Sevilla.

Do keep in mind that Puerta de Atocha's train station is HUGE.

If you decide to take the Cercanías train from the airport (designated [on the diagram linked above] as a backward white "C" within a red circle) you will arrive on the lowest level of Atocha, & you'll need to go the upper level to find the AVE waiting area.
Once you find your train number posted on the electronic arrival/departure board, you will get your ticket scanned, then will take escalator down to the train's platform. Your luggage will have to go through a security check (x-ray machine) at some point before boarding the train.

Great advice by Ang84335:

If you already have your ticket to Sevilla, a transfer from the airport to Atocha on the Cercanias is included.

You can read about the Combinado Cercanías here

Have a wonderful trip!