Kerala is a compact state and getting around is straightforward, if not always fast.
Trains are the most comfortable way to cover longer distances. The main line runs along the coast from Thiruvananthapuram through Kollam, Alappuzha, Ernakulam (Kochi), Thrissur and up to Calicut and Kannur. Trains are frequent and very cheap. For short hops within Kerala you can usually just turn up, but book ahead for longer journeys or travel to neighbouring states.
Buses go everywhere, including places the trains do not reach. The state-run KSRTC buses are reliable if basic. Private buses are faster but more chaotic. Expect crowding on popular routes. The bus network is the only practical way to reach hill stations like Munnar, Wayanad and Periyar.
Taxis and auto-rickshaws are widely available. At airports, use the prepaid taxi counters in the arrival hall to avoid haggling. In towns, auto-rickshaws are cheap for short trips, but agree on the fare before you get in or insist on the meter.
Driving yourself is not recommended unless you have experience with Indian roads. Traffic is dense, the roads are narrow, and the driving style takes getting used to. Hiring a car with a driver is a much better option and surprisingly affordable for multi-day trips.
Boats are the way to explore the backwaters. You can take the public ferry between Kollam and Alappuzha, hire a houseboat, or arrange shorter canoe trips through the narrower canals. Around Kochi, local ferries connect the islands and peninsulas that make up the city.