In order to take part in any paid employment in Colombia it's necessary to apply for the appropriate visa through Migración Colombia; your employer will need to sponsor the application which is more likely if you have formal qualifications and are willing to commit to a longer contract.
There is a growing demand for qualified English-language teachers in Colombia. Some schools may be willing to pay cash-in-hand for a short period of time, but for longer-term employment you will have to find a school willing to organize a work visa. Don't expect to get rich teaching English: you're unlikely to make more than a few million pesos a month, and usually much less.
As a general rule, the more popular the city is among travelers, the harder it will be to find employment.