Remember, if the work you would like to use is in the public domain or openly licensed, you do not need to ask for permission to use the work. You also do not need to ask permission to use a work if your use falls under one of the copyright exceptions, such as the TEACH Act or fair use. However, if you aren't sure if your use is allowed and you are able to obtain written permission from the copyright holder for your specific use, you can be sure that your use is legal.
The challenge is that it can be difficult to determine or find the copyright holder. If the author's name is not listed with the work, you may have to do some research. Even if the author's name is listed on a published work, the publisher may be the actual copyright holder, so you might want to start there.
You may also contact the Copyright Clearance Center (CCC) to see if you can pay a royalty fee for use of the work. This can be costly however, as there are usually fees in addition to the royalty charges. The CCC likely will not tell you if your use is covered by a copyright exception, so check carefully before paying these fees. You may also want to check with the library about your use first.
If you are able to contact the copyright holder, make sure to obtain written permission for your specific use. Be very clear about how you would like to use the work, and consider future uses that you might make (so you don't have to ask for permission again). Keep a record of your interaction with the copyright holder.