This is a complex question and the answer depends a bit on how in depth your research needs to be.
If you're just getting started, it might be useful to visit the Intellectual Property page on the Libraries' Entrepreneurship LibGuide. There you'll find introductory information and a collection of free resources.
If you're getting into more specific research regarding a particular patent/trademark you're interested in filing for, then you'll likely need to visit the U.S. Patent and Trademark Office website and it's likely you may eventually need to go to a Patent and Trademark Resource Center.
Make an appointment with a 