Car is the best way to get to and around Chettinadu. Renting one with a driver from Trichy, Thanjavur or Madurai for two days costs around ₹7500. Or take a bus to whichever town you'd like to stay in – or as close to it as you can get – and hire a car there for day trips, for about ₹2500 per day.
From Trichy, buses run every five or 10 minutes to Pudukkottai (₹44, 1½ hours) and Karaikkudi (₹90, two hours); you can hop off and on along the way. From Madurai, buses run to Karaikkudi (₹95, two hours) every 30 minutes. There are also buses from Thanjavur and Rameswaram.
Three daily trains connect Chennai Egmore with Pudukkottai (sleeper/2AC/3AC ₹265/720/1035, six to eight hours) and Karaikkudi (₹280/775/1085, 6½ to 9½ hours). One train connects Chennai with Chettinad Station, for Kanadukathan (₹275/745/1070, nine hours).