IIT Madras is located in Chennai, Tamil Nadu, which is well connected with major cities by train and air routes. The website for Indian Railways and several flight booking websites contain up-to-date information about travel options.
From Chennai Central Railway Station: You have multiple options. If you take a taxi, it would cost you maximum INR 400. An auto-rickshaw may cost around INR 250. A bus would cost INR 10, and a local train (from Park Town to Kasturibai Nagar) would cost around INR 6. Reaching the Park Town station from the Chennai Central requires a few minutes walk after crossing the main road. Reaching IIT from Kasturibai Nagar stop requires 10 minutes walk along Sardar Patel Road.
From Chennai Airport: You can get a pre-paid taxi which will cost around INR 700. The taxi can drop you directly to the IIT hostel. The taxi would have to make an entry at the IIT Main Gate at the Security Desk.
For transportation inside IIT, one can either walk or take the IIT bus which runs inside campus every 15 minutes free of charge for everyone. The bus runs between 06:00 and 22:00 hours. It can be used to reach the hostel from the main gate and to reach the department from your hostel etc.
CSE Department can be entered from two sides. First, which is the CSB (Computer Sciences Block) side, is closer to the hostels and is beside the P G Senapathy Centre for Computing Resources, also called as Computing Center (CC). The bus route for this CSE door is Hostel - Gurunath shops - Taramani Guest House / Gym - CSE Department / CC. Second, which is the BSB (Building Sciences Block) side, is off Alumni Avenue (between Velachery Gate and Gajendra Circle). The first two floors of BSB are occupied by the Civil Department, while CSE is located at the second floor (connected to CSB via a corridor from the second floor). The bus route for this side from Velachery Gate is Velachery Gate - BioTech Department - CSE / Civil, while from Gajendra Circle, the route is Gajendra Circle - Admin Block - CSE / Civil. More information about the IIT bus is provided here.