How much US cash can I bring into Chile? How would you find the answer to this question for other countries?
This forum states that you can bring in US$10,000.
However, it's often pretty hard to find, as there's not always a universal website for these things.
For a lot of immigration/travel/visa stuff, VisaHQ.com is the place to go - for example, their Canadian page tells you that you can bring in or take out up to $10,000 Canadian before you need to declare it. However, try their Chilean page and there's no mention of restrictions on money.
Other times it'll be on the relevant country's embassy or high commission webpage.
Or else, you can always ask here again! ;)