The intercity bus from Chennai (Koyambedu bus terminal) takes about 2 hours. You'll find one (non ac express/ordinary services) leaving every 15 minute or so. AC bus services operate from the T-Nagar bus terminal every hour.
From Chennai Beach station you can also travel to Kanchipuram by the local train (EMU service)
Chennai to Kanchipuram Road Route:
Chennai--40km-->Sriperumbudur --32km--> Kanchipuram
Kanchipuram in Tamilnadu is located 72km southwest of Chennai. Also Kanchipuram by road is 70km and 280 km east of Vellore and Bangalore respectively.