Apply for residency in colombia

Probably the best thing to do is head over to a local immigration office and ask them the process of extending your tourist visa.  It can be a different process for each citizen type (USA, Canadian, Indian, Chinese, etc). 

Most times you just need to pay a fee and explain why you want to extend your tourist visa and they will give you additional time.  Sometimes they will ask you to leave for 1 day and come back to renew your visa.  If you are looking for a work visa, that is a different process and you will likely need a work contract to help you apply for the visa but you might have to leave the country and re-enter.  Residency will require 5 years.

The simplest way to extend is get married.  You can then get a Visa good for 3 years and you will be able to work normal jobs, that don't require a degree (Doctor, Lawyer, etc).  With this visa residency will require 3 years.  If you have a child with your colombian partner, than residency will be granted immediately after you fill out the forms.  You will then need to renew your ID every 5 years.

This information is just generalized information to give you an idea.  Some people can have special circumstances or be eligible for different visa programs, etc.  You just need to check with your local office and visit their website to double check anything they tell you.