The natural paradise that is the Galapagos Islands is not just a must-visit destination in Ecuador, it is one of the world's most wonderful and important natural sights, containing wildlife that you simply cannot find anywhere else. Travel from Quito is usually via Guayaquil, the big port city in Southern Ecuador which sits much closer to the islands. Arrival onto the islands is normally through the island of Santa Cruz and its Baltra Airport, or the island of San Cristobal and its San Cristobal Airport.
Travel to the islands is via plane and (occasionally) boat. Although you could travel part of the way from Quito to Guayaquil by bus or by train, there is little point if your primary goal is getting to the Galapagos, because you will have to switch to plane or occasionally boat) there regardless. Flight prices are not significantly cheaper from Guayaquil to the Galapagos than they are from Quito to the Galapagos and flights from Quito normally stop in Guayaquil en route to the Galapagos anyway.
If you are visiting the Galapagos but wish to travel through Ecuador first, see this article on how to get from Quito to Guayaquil, with transport options including bus, train and plane.
By Plane
Duration: 2.25-4 hours
Quito's new Aeropuerto Internacional Mariscal Sucre is one of South America's best and biggest airports, 23 miles outside Quito.
Avianca or Latam run a direct non-stop flight to Baltra Airport on Santa Cruz Island most days (except, currently, Thursdays and Saturdays). Many other flights run daily with a stop-over in Guayaquil Airport to allow more passengers to board, and the difference in time can be small if you plan it carefully: 2.25 hours direct or as little as 3.5 hours inclusive of a stopover in Guayaquil.
To get to San Cristobal Airport on San Cristobal Island, flights (also with Avianca or Latam) are almost all via Guayaquil Airport, with a stop there to pick up more passengers.
The overwhelming majority of visitors arrive on the islands by plane.
By Boat
Few visitors arrive on the Galapagos by boat, because the crossing from the mainland is long and rough. Galapagos Island cruises embark from the islands themselves and, in any case, a boat journey to the Galapagos will reveal few sightings of wildlife until you actually arrive there.