You'll need to share more detail, there's a lot to something like this. Surely you're not asking someone to write down every single step? What have you tried? Where are you stuck?

At the very least you need page(s) with form(s) that will submit the data to a backend system. So you'd have to know what sorts of server side languages your hosting provider supports.

Are the students using this in the classroom or on their own? If on their own, you likely need a database of user names and passwords, otherwise you could run into all sorts of cheating.

Do they have to finish it in one session or can they leave and come back? Is there any sort of time limit?

And so on and so on.

Your best bet is to look up scripts to send email and work your way backward from there.