There are a number of different options for getting to El Encanto Hotel in Cahuita:
The public bus is the most economical (about $8pp) and is quite easy. It leaves 5 times daily from the Caribe Sur Bus Terminal in San Jose at 6am, 10am, Noon, 2pm and 4pm. And there are also additional frequent buses as well that go to Limon where you can transfer to Cahuita. Please note that during peak periods these buses do sometimes sell out and you can only buy tickets in person at the bus terminal so if you can get there the day before to get your tickets, that is best.
If you're coming straight down to the coast from your international flight and would prefer not to spend the first night in San Jose, the best option is often a private driver that meets your flight and will bring you directly to El Encanto. There's no waiting for a scheduled departure, no luggage restrictions (they use a roomy 10 passenger van and even bigger vehicles are available if you've got a big group) and no stopping along the way for other passengers. They also can take you from any other place in Costa Rica (e.g. Arenal to Cahuita or vice-versa).
Shared ride van services are comfortable and pick you up right at your hotel and will bring you right to El Encanto. They travel around Costa Rica on a scheduled basis. We find the most reliable to be Interbus. They will not transport pets, you will need the private driver option for that.