You can fly to the Galapagos Islands only after first traveling to Quito or Guayaquil in mainland Ecuador.
Various international airlines fly to one or both of those cities. For flights from many U.S. cities, American Airlines offers the fastest and most convenient flights to Ecuador. Often your journey requires only a quick connection in Dallas or Miami. Click American Airlines to view its website and schedules.
Some U.S. cities are better served by other airlines. For example: Houston (Continental) and Atlanta (Delta). Iberia and KLM have direct flights from Europe.
TAME and Aerogal are the two major airlines providing air service from Quito and Guayaquil to the Galapagos Islands. The flight takes about 2 to 2.5 hours and the roundtrip fare is around $450 ($400 in the low season).
It is almost a certainty that you will need to spend one night in Quito or Guayaquil before your Galapagos flight day because planes to the Galapagos Islands leave in the morning, before nearly all the international flights arrive. As a bonus, the overnight helps insure yourself against the negative repercussions of a lost bag or delayed incoming flight.
Make it two nights if you want to take a full-day Quito city tour. But don't add the extra day if you are laying over in Guayaquil. That city has little to do or see.
You will likely also have to spend a night in Quito or Guayaquil on the way home because the flights from the Galapagos Islands usually arrive too late to make your return flight home.
This Inca ruin ranks number 7 on my Top 100 World Wonders list for good reason. Machu Picchu is spectacular and stirring and should not be missed. Some travelers make a pre- or post-Galapagos side trip to Machu Picchu. This requires a south-bound trip to Peru, which borders Ecuador. If you're buying a packaged Galapagos tour, your agent can easily tack Machu Picchu onto it.