As the author of a thesis, you own the copyright to your work. Under U.S. Copyright law, a creator of an "original work" created in a "fixed tangible medium" is immediately and automatically the copyright owner of the work, and the work is protected.
As stated above, your thesis is automatically protected under copyright. However, there are some important practical and legal benefits to registering your copyright, particularly the right to collect "statutory damages" in a successful infringement lawsuit. Essentially, if at some point you might want to take legal action in order to protect your work, you should register it with the U.S. Copyright Office.
In the course of this submission, you can request that ProQuest/UMI file for copyright with the U.S. Copyright Office on your behalf. ProQuest charges a $55 fee for this service. You can also do the filing yourself directly through U.S. Copyright Office at copyright.gov. You will be charged a $35 registration fee.
For help understanding fair use, please consult Hood College's Copyright Policy. Guidance on obtaining permission can be found at Columbia University and from the U.S. Copyright Office.