Chennai has a functional suburban rail network that's the most useful option for getting around quickly. The MRTS (Mass Rapid Transit System) runs along the coast from Chennai Beach south to Velachery, covering Mylapore, Thiruvanmiyur, and other useful stops. The Chennai Metro now covers significant sections of the city and is the easiest way to cross the city without getting stuck in traffic.
Auto-rickshaws are everywhere but negotiate the fare before getting in — meters are rarely used willingly. App-based taxis (Ola, Uber) work well and are usually more straightforward on pricing.
City buses are cheap but crowded and difficult to navigate without knowing the route numbers. The suburban trains are more useful for tourists — they run frequently, are inexpensive, and cover the main tourist corridor along the coast.