How can I continue my journey to Shenyang from Beijing?

I am arriving at Capital Airport Terminal 3 on Saturday, 12 June 2010 at 08.50 morning and I want to continue my journey to Shenyang. Is there a train inside the airport going to Shenyang? If not, where in Beijing can I go to catch a train? I mean in which railway station shall I go and where is it in Beijing? If I go by taxi from Terminal 3 to the railway station, about how much does it cost. Are the fares and the timetables above accurate?
Can I go to Shenyang by airplane? What time does it depart and from which terminal in Capital Airport and what time does it arrive in Shenyang and what is the fare? How can I buy tickets? XIE XIE.