How will I know if someone signs up for a class

I made a registration form so I can keep track of students signed up for an upcoming course, how do I know when students sign up?

IS there a roster I can view?

I inspected your form and it does not have an Email Notification. Considering that all forms by default have an email Notification, I assume that you deleted your Notification. 

If you want to receive an email each time your form is submitted, you need to setup an Email Notification inside of your form. Inside of this guide, you can find how to do it:

Setting up Email Notifications

You can also view submitted data on the submission page of your form:

How to View Form Submissions