Copyright is one of those ugly messes that few truly understand and everyone has a differing opinion on what is "right" and "legal." With that caveat, I'll plunk down my two cents, based on many years in publishing (both print and digital):
Generally speaking, you cannot directly copy a full article (no matter how much credit you give), but you may quote from it (with credit of course) - there is a vague definition of reasonable use. So, if you're writing an opinion piece, discussing things you've learned, or read in the news, and you quote sections of their piece, it's appropriate. So long as that's not the "meat" of your own piece.
Crediting where you learned something is not required by law - if you are not substantially copying their content, and you are simply creating your own thoughts based on information gathered. If you are citing studies, quoting statistics, figures, etc, then you should certainly footnote those things if you want to be absolutely proper.
Copyright does apply to blogs - just as anywhere else. US Copyright info:
Many sites have the ability to directly copy content into your blog (ie: the LA Times offers a blog this feature which embeds the story into your blog, with their links and feed built in.) If you use that type of feature - terrific. Otherwise, it's back to standard rules apply.
Best of luck!