The most common way is to take a public minivan. There are minivans leaving from Bangkok at Victory Monument from early in the moning until 7 o'clock in the evening.The price is just 60 Baht per seat, so you can buy an extra seat for your luggage. Depend on the traffic the trip takes about 1-2 hours. They should drop you of at the Jao Phom Market in the center of Ayutthaya. A Tuk Tuk drive from there to our Homestay shouldn't cost more then 100 Baht.
The train isn't the fastest way to Ayutthaya but it is almost the nicest. The trains leave regularly from the Hua Lamphong Station in Bangkok which is connected to the MRT (subway). The price is about 15 Baht and it takes around 2-3 hours depend on the type of train. A good price from the trainstation in Ayutthaya to our homestay is 120 Baht
An Taxi is most comfortable way to go to Ayutthaya. The price is about 1500-2000 Baht depend on the driver. Please make sure you handle the price clearly with the driver before the taxi leaves. If you don't agree with the driver you are free to leave the taxi and take another one.