Due to connectivity issues getting to San Andres used to be hard, nowadays you can get here from pretty much everywhere in the world.
By Plane from Colombia
Numerous airlines fly to San Andres with Daily flights, Copa Colombia formerly known as Aerorepublica flights from daily from Bogotá, Cali and Cartagena they also flight from Barranquilla 3 days per week. Another airline that flights to San Andres is Avianca, mistakenly considered pricier than Copa Air flights 3 times daily from Bogotá.
Lan Airlines flights daily from Bogota and 3 times a week from Cali at some really crappy times.
A new low cost airline named Viva Colombia started flying to San Andres from Medellin and Bogota, they offer some extremely cheap deals if you book in advance, but expect to be nickled and dimed for everything. As an example your carry on can weight a maximun of 6 Kilos and they are very strict about it. People holding foreing credit cards always have a hard time booking with this airline on their website as they only accept reservations done in their call center, if you are already in Colombia they give you an array of options to pay offline, like bank deposit and at Balloto tellers.
By Plane from Abroad
COPA airlines is the only airline that flights twice daily from Panama making it easy for international travelers to reach San Andres. Several airlines flight seasonly from Abroad, that is the case of Air Transat and some European Airlines, you might also want to check with your local travel tour operator as we receive many charters from Peru, Ecuador, Costa Rica, Salvador among others.
Most airlines flying from abroad will have connecting flights in Bogota, generally the layovers are around 6 hours which give travelles plenty of time to go and explore La Candelaria which is the old district of Bogota that's close to the airport.
If you are traveling the Colombian or the central american coast and you happen to be a really lucky person, you might be able to catch a ride in one of the many yacht that come to the island, in my lifetime I have only seen 2 people pull this stunt, try your luck.
If you are not that lucky you may want to try the cargo boats, they sail bi-weekly from Cartagena and Barranquilla to bring goods to the island check with the dock, I cant really assure you you can do this, but I have met a couple of people who have done it.