Although you may make initial contact with a copyright owner by phone, you should secure permission in writing. Publishers and licensing agencies may have a form that they prefer that you use for requesting permission. Keep careful records of your correspondence in seeking permissions.
Your written request should be as specific as possible and include:
Keep A Record!
Lastly, be sure to keep a copy of all permissions and license agreements! Having a written record can be invaluable if questions or disputes arise down the road, and allow you to demonstrate to others that you have the legal right to use the owner's work (particularly publishers, who will often require written proof that permission has been obtained).
Although getting written permission from the copyright owner is your best bet, permission does not have to be in writing. If you aren't able to get something in writing, document your conversation. You may also want to send a letter of confirmation to the owner setting out your agreement.
In some cases, you may never get a response from the copyright holder -- you may never even be able to identify who they are or how to contact them! It can be difficult to know how to proceed when you reach a dead end. Unfortunately, no matter how diligently you have tried to get permission, these efforts cannot completely eliminate the risk of infringement should you proceed to use the work.