What Anthony said, but with more emphasis, especially with puzzles, you should try to acknowledge the composer. There should not be any possibility that anybody could think you claim the work as your own.
If you do that, you can post whatever you like
Hi there. I have been taking games and puzzles out of chess books and turning them into puzzles on the computer. It makes them easy to scroll through and revisit. If I post these to a blog on the site, is that plagiarism? In general, chess games seem like public domain. What about puzzles?