Can anyone tell me what is the policy on a use of a quote on t-shirts. I have a quote by Calvin Cooledge that I like and would like to put in on a t-shirt. However, I am a newbie and do not know the copyright restrictions on using quotes if there is any.

It would be nice if there was an easy answer "Yes you can" or "No you can't" No such luck.

CP policy is not to violate copyright law. Quotes fall under the same umbrella as other copyright issues. Whether you can use them depends upon their source, their age, your use and other considerations.

Public domain is fine, if you can prove it is public domain. Licensed or permissive use is fine, as long as the terms are met. Copyright is not the only issue. Quotes from a sitting President would receive different analysis from quotes of the same individual before and after holding political office. "Fair use" is a defense to infringement. It means that infringement has occurred but is excused for public policy reasons. Fair use is not so easy to show on products for sale, not impossible, but difficult.

Understanding copyright, trademark, and rights of publicity/privacy is critical for everyone involved in CP. Below is a resource for learning about copyright issues.
http://www.tutortanith.com/resources4.htm#law