If you are a first time visitor, avoid the public transport. It is very congested and takes lots of time to travel.

Take the 3 wheeled autorickshaws or Call taxis. The former is cheaper, but remember to bargain. Some tips for travelling by autorickshaw are:

 

  • The cost for an autorickshaw ("auto") should be about Rs.10 per kilometer (and sometimes 10-20 rupees above that price). It pays to look up the distance on Google maps beforehand because they are notorious for refusing to put on the meter and cheating you, charging up to twice the appropriate price.
  •  Try to hail autos off the street rather than a stand, as those at stands will collude to drive up the prices. 
  • Clearly state where you want to go, don't get in if they don't recognize your destination quickly, and always bargain before getting in. Some will try to ask for more money halfway to your destination; refuse this request and hold your ground, unless the traffic is horrible or you gave them the wrong directions and they went out of their way to find your destination for you. Some will intentionally get "lost" or ask for a "night surcharge"; if you were clear about the price you were paying when you got in and gave good directions, there is no reason why you should pay extra.
  • Most importantly, look up key landmarks near your destination address if it's not a famous site. Rather than the street number, know the name of your target road and neighborhood, and also nearby things like subway stations, banks (e.g. ICICI), grocery stores (e.g. Spencer's), and restaurants (Apoorva's Sangeetha, Murugan Idli, etc.).

 

 Once you know these autorickshaw drivers they can literally be your guide to the city. Most of them have a good knowledge of the city and guide you to the major attractions, The Marina Beach and lighthouse, Gandhi museum, Fort St.George, War memorial, among others. If you find one you like, ask for his mobile number and avail his services again.

Most Chennai hotels catering for tourists also can arrange transport. This is the hassle free option - but not the budget option.