Although I was on an organised tour, for the independant traveller, buses travel to Kumily from most of the major towns in Kerala and Tamil Nadu.
Ernakulam ( near Cochin) 6 hour journey 10 buses daily ( 3 are express)
Trivandrum 8 hour journey 2 daily
Kovalam 9 hours 2 daily
Munnar 5 hours 5 daily
Kottayam 4 hours 7 daily (express)
From Kumily to Periyar there is an irregular bus service, or plenty of auto rickshaws/ jeep taxis to hire for the 4km journey if you don't fancy walking.
To get to the sanctuary you'll have to go to a town called Kumily. From there you can walk or take a rikshaw to the sanctuary.
I took the bus from Kottayam to Kumily. (42 roepies). The road is very curly, and it is a pretty rough drive for 4 hours. But at the end the scenery is very beautiful.
From kumily I took a bus to Cochin (Ernakulam)(96 roepies). This took 6 hours but the seats where a bit better.