The name of the market sound almost same like the name of Ayuthaia province so it is easy to remember for this reason. As for the directions to Ayothaya floating market just look north of bankok about 70 KM - you can take a taxi or drive your car there. Parking available near the market for about 20 BHT per day.
A lot of souvenirs can be found while walking among the shops and restaurants of the floating market.