Is it OK to take small pieces of content (maybe a few paragraphs of text, not the full page) and put it on my site, then have a link at the bottom directing the reader to the original page to read the full content? For example news stories, could I take the headline and the first wee bit of the story and then link back to the original news story?
It's always best to ask permission first. Most sites would gladly allow you to do what you are proposing. Others might dislike it and even take legal action against you, so the best and only surefire action to take is to ask permission first. Just because another site is doing it, doesn't mean that you can too. You never know what deals or arrangement the other site has with the original source site.