There are regular international flights into major cities including Bogotá, Medellin, Cali, Barranquilla, Cartagena, Pereira and San Andres Islands as well as to other smaller cities in the borders with Venezuela and Ecuador.
There are daily direct flights to and from the U.S, Canada, Mexico, Costa Rica, Panama, Spain, France, and South America.
Taxis are regulated, reasonably priced and safe from the airports. A taxi ride from the airport to the central business district in Bogota, takes approximately 20 minutes.
Enter from Venezuela by the San Cristobal-Cúcuta / Maracaibo-Maicao pass.
Enter from Ecuador by the Tulcán-Ipiales (Rumichaca) pass.
Connections can be made from the Caracas main terminal to most cities in Colombia. From the main terminal, Maracaibo (Venezuela) you can find buses that run to the cities (Cartagena, Baranquilla, Santa Marta) on the coast. The border at Maicao provides a relatively easy, straightforward entry into Colombia from Venezuela.
It is very straightforward to enter Colombia from Ecuador. Travel to Tulcan, where you can get a taxi to the border. Get your exit stamps from the immigration offices and take another taxi to Ipiales. From there you can travel further to Cali, Bogotá, ...
You can't cross from Panama to Colombia by bus--the Darien Gap begins at Yaviza, where the Interamericana runs out.
Most Western countries don't need a visa. American citizens do not need a visa unless they are staying for more than 90 days. Colombian authorities will give American citizens an on-arrival visa free of charge, which is printed onto your passport and lets the person stay for a maximum of 60 to 90 days. It's very hard to get 90 days tourist visa on arrival. Immigration officers will ask you to show all the tickets of your route for it. Irish citizens do not need to apply for a visa at a Colombian embassy anymore, and should have the same treatment at entrance as any other traveler from other part of the world.
You can apply for a one-month visa extension at a DAS-office in most cities, which costs around COP $60.000. You need two copies of your passport's main page, two copies of the page with the entrance stamp, two copies of a ticket en route out of the country, and four photographs. The procedure takes some time and includes taking your fingerprints. The maximum length of stay can not exceed 6 months in 1 year with a tourist visa.