The main international airports are in Bogota, Medellin and Cali, but Cartagena also hosts international flights. If you’re doing the South American backpacker trail, there are land crossings to Ecuador and Venezuela. However, the south of Colombia is best avoided, so if you’re heading in that direction (ie towards Ecuador) flying is your best bet. There are no land crossings into Panama.
Check travel advisories before heading to Colombia, because some parts of the country are unsafe, so long distance bus rides can be a no go. Those that are OK will be long, and over bad roads. Flying is your best option to get around the country.
In the big cities, avoid jumping into a cab hailed from the street on your own. The best idea is to ask at a big hotel for the number of a taxi company, which you can then call to come and meet you.