You can get to El Chato from Puerto Ayora by bike, bus, cab, or tour, but the easiest way is by taxi. This takes approximately 45 minutes and costs around $40-$50, including a stop at Los Gemelos (Twin Craters).
Taking a bus ($1) to Santa Rosa and walking 2.5 miles to El Chato is the cheapest option.
For maximum time efficiency, combine a visit to El Chato Ranch with an airport pick-up or drop-off.