You SHOULD do something = it is a good thing to do
(because it is the Right thing to do).
Brasília is a very dry city, you should drink a lot of water in order to avoid dehydration.
According to the doctors, we should eat more fruits everyday.
You should pay your bills in advance in order to avoid paying interest.
The Government should do more to improve education.
You SHOULD NOT do something = it isn't a good thing to do
(because it is probably Wrong).
You should not believe everything you read in the newspaper and watch on TV.
People who live in apartments should not speak up or make loud noise after 10PM.
"She shouldn't bring her little children to our meetings."
"Shhh! We shouldn't make any noise, this is a hospital"