You will need to add a domain, or sub-domain, for each of those users. If you want to do it without any additional costs for domain registration, you can put these subdomains under your own domain (such as student1.yourdomain.tld, student2.yourdomain.tld, etc) or you can build them under the "dreamhosters.com" subdomain (which DreamHost lets you use at no addtional charge for this purpose).
You can set all of this up from the control panel, domains, add a domain/subdomain screen. Just specify that a given domain is to be run under the user you desire.
So, if you have a "new user" named "user2", you can add the subdomain "something.yourdomain.tld" or "something.dreamhosters.com" to your account, and assign that domain to be controlled by/run as user "user2".
Note that, by default, you will not be given the passwords for these accounts, so I recommend before you presetn credentials to a student, you change the password for that user, record it so you know what it is, then give them their credential with the password you assigned. THis makes it easier fro you to login to and manipulate (if need be) files in "their" user area.
That is optional; you can always change the password at any time to allow yourself iun , and lock them out, should you need to - I just think in the situation your describe, it is easier if you manage the credentials (at least initially).