Ayutthaya is an easy trip from Bangkok. Trains run frequently from Hua Lamphong station (about 1.5 hours, under 100 baht for third class). The train also stops at Don Mueang station, opposite the airport, so you can head straight to Ayutthaya on arrival.
Air-conditioned buses leave from Bangkok's Northern Bus Terminal (Mo Chit), near Chatuchak Weekend Market. The ride takes about an hour and a half depending on traffic.
Minivans are faster and depart from Victory Monument. They are more cramped but get you there in about an hour. From Ayutthaya's bus or train station, a tuk-tuk to the historical park takes ten minutes.