Fort Kochi itself is small enough to explore entirely on foot. Renting a bicycle is the easiest way to cover the area and cross into Mattancherry — several guesthouses and shops on Princess Street rent them by the day for around 100 to 150 rupees.
Auto-rickshaws are available throughout the city. Agree on a price before getting in, or insist on the meter. The ferry between Fort Kochi and the Ernakulam mainland runs frequently and costs just a few rupees — it's one of the best value journeys in India.
For exploring the wider city — the shopping areas of Ernakulam town, the bus stands, the railway station — the ferry followed by an auto-rickshaw or Ola/Uber is the most practical approach. Kochi's road traffic can be heavy, especially in the Ernakulam commercial district.