While most grants are aimed at researchers past the doctoral stage, there are some "pre-doctoral" grants to fund research towards a doctorate and even fellowships to support doctoral research.
So while many of the grants listed on the sites might not be applicable to you, depending on research area or stage of the dissertation you are at, it does pay to be aware of the major funding agencies along with the basic requirements of a grant application.
Of course, there are more than just grants, there are also fellowships and other scholarships that you might help fund your graduate education and research. Make sure to explore all available opportunities.
In November 2021 as part of the Graduate Student Association Professional Development Seminar, Dr. Anna Bukiya of UT-Health Sciences and Dr. Michael Harris of UofM talked about how to write grant proposals, where to look for opportunities, and why it is important to get started now as a graduate student.
Finding, Researching, and Writing a grant or fellowship application can be hard, especially if it is your first time. These campus centers can be great assets for you!
Some grants have requirements for preservation of data collected during the grant, along with open access for elements. Below is an example from the NIH of this, along with other useful links, including UofM's Digital Commons repository.