In some books it's like this "blah blah" in other books it's like this 'blah blah' Which one is correct?
In the USA and Canada, it's usually "blah blah." In the UK and other parts of the English-speaking world, it's 'blah blah.' So they're both correct, but it depends on where you are.
yup!... but it doesn't really depend on where you are, only on where you want your writing to be published...
The tricky thing is differences in punctuation before/after the closing quote. I think I'm going to switch to single quotes so that my punctuation is more consistently UK.