Can I hand out students a few pages from books as supplementary materials? No textbook is perfect. So if I want to supplement my course with some material (a few pages from different references every now and then, on topics I find lacking or weak in the textbook):


is it legal to make copies of those a few pages and give them to the
students as hand outs? 
is it legal to scan them and upload them on
the course site? 
should I email the authors to take their permission
1st? what if one author is dead? 
in case the above is a violation of copyrights so what should I do then? asking the
students to go read those parts in the library? (the students would need to keep a copy
of the reading/supplementary materials)
First, in most cases, the channels through which you distribute the material to your students (hardcopies, restricted-access course website) is not important. Secondly, the copyright holder for each work is (again, in most cases) the publisher, not the author. Thus, getting permission from the author is not necessary.

So, the surest way to avoid trouble is to secure the permission to reproduce the content from the publisher. Publishers should have an online page (e.g., see here for the American Chemical Society publications) explaining how to obtain this permission. Many academic publishers nowadays rely on a centralized online service called RightsLink, where you can directly select the material you want to reproduce and the conditions in which you will use it:

       

The tool then tells you if you can get a permission to reproduce at no charge (it usually is if you want to reproduce only small parts, a few figures) or if you would need to pay.

Finally, under US law you may qualify for a fair use right to reproduce parts of a copyrighted content.