Christian Medical College (CMC) Vellore is one of the famous hospitals in India is located in the south Indian state of Tamil Nadu. The hospital can be reached by various ways but here we will look into two of convenient ways.
First one is via flight. Travel up to the airport at Chennai (http://www.chennaiairport.com/), then book a prepaid cab and travel to the hospital directly. From this Airport to the CMC will take about 2 to 3 hours, depending on the pressure of traffic on the roads.
Alternatively you may travel to the Chennai Central Railway station from the airport at Chennai and get a train for a railway station called Katpadi. After reaching Katpadi you may take an auto rickshaw to CMC, it takes about 20 to 30 minutes.
Katpadi is connected from various parts of India via railway, so you may travel by train instead of air. You may choose to travel directly to Katpadi or you may travel up to Chennai Central and then travel to Katpadi by another train.
For train options you may try to visit this website https://www.irctc.co.in/
This piece of travel guide is based on experience of the author. You may cross check them from other sources too.