score:2
There's no one answer to this question applicable to every place on the planet and, really, it's just common sense. :)
Every big city will have service providers that can get you a long-stay, at a price, but for less then the cost of a hotel.
If you speak the language and can put in the time, finding your own place will obviously be cheaper.
AirBNB and its cousins give good shorter term solutions and, sometimes, provide great steals. Also realise that, for plenty of accommodation on AirBNB, monthly rentals are available.
Lastly, hotels, hostels, as well as couchsurfing, provide good short term accommodation at a relatively high cost.
So, not knowing where in Colombia you're going, and only considering cost, it seems to make sense to book a hotel, hostel or AirBNB place in advance, for a week, say, and then to look for more permanent accommodation while you're there.
Upvote:1
My suggestion is to book something for 1-2 weeks on airbnb, at a hotel or hostel, or something similar. Then, during your first couple of weeks there, make some connections and look for people renting a spare bedroom.
I've never been to Colombia, but I've done this in Mexico, Portugal and Cuba with good success.
How to find rooms for rent varies greatly by location, but in general, ask around. If you don't speak Spanish (you should consider learning at least the basics), you can likely find an expat community in any large city (try meetup.com and couchsurfing.org as examples). There, ask around--where are others staying? How do you find a place to live for 6 months?
With those connections, start making calls (by phone or in person) to see what's available, and find something you like.
You can start a lot of this before you arrive--at least the networking part with expats, so that you'll spend less time looking once you arrive.
In summary, there's no exact formula for this, but in general what I do: