It is also possible to take a bus to Thumbal (there is a bus from Salem almost every hour via Thumbal), but buses from Thumbal to Sittilingi are less frequent - not the recommended choice for first-timers).
Sittilingi is also well connected to Morapur, a station on the main Chennai Salem line. However you might want to come via Salem, which is a better and shorter option, if your timings are ok. Trains from Chennai stopping at Morapur [from where you can get a local bus to Harur]
Yercaud Express [Morapur arr.0430]
Kovai Express [Morapur arr.0955]
West Coast Express [Morapur arr.1530]
Buses From Harur
To Sittiling - 0515,1030,1305,1530 hrs
To Kotapatty - almost every hour from 0530 to 2130 hrs
Travel Times - Bus
Salem - Sittilingi (via Vahzappadi) 2 hrs 30 mnts
Kotapatty to Sittilingi - 20 mts (10 km)
Salem to Harur – 2 hrs
Dharmapuri to Harur – 1hr
Harur to Sittilingi – 2 hrs