I created a form for students to submit their assignments. They copy their URL of the Google document, then paste it in a form. When I get their responses, I can't open their URL, it says I am not granted access. I checked the form and I am the owner and have access. What do I need to do?
It sounds like you have two different Google Documents. You have the Google Form that you created and the Google Document that each of your students created with their work.
You have permission to your own Google Document form. But you need permission to access your students' Google Documents work product. Just because you have the link to your students' Google Documents doesn't mean you have permission to access them.
Your students need to change the permissions on their Google Documents. Your students need to click on the "Share" button in the top right section of their Google Document, and add your email address to the "Invite people:" field.
@jaredcohe is correct, your students should share the document with you. They should follow the step by step procedure described below:
Click Share & save!
If you don't want to go to the trouble of having students "share" the assignments, they will have to make the assignment "public", if your school allows that. Doing so will allow the URLs to work.