While on the Ecuadorian continent, there is full phone and cellular service, though you must check to see whether you can use your particular provider. Generally, it is most economical to use calling cards. Also, there are internet wifi cafes available.
Once on the Galapagos Islands, internet service and even telephone is generally not available except in the ports of Puerto Villamel, Puerto Baquerizo Moreno and Santa Cruz, where you may have access from your cell phone with a calling card or from an internet cafe. One of the delights of being in Galapagos is removing yourself from the sound of the telephone and pull of the internet. If you do need service, make arrangements at home with your carrier. Many of the hotels, including Galapagos Eco Friendly, offer wifi service. If you must use wifi and internet, be prepared for delays. You are most definitely not in New York City!
For more information on communications in Galapagos read our Publication, Nature Interpreter on Medium.com.