Sorry for the ignorance displayed in this post, but I was unable to find any answers to these questions by searching on Google.

How do web hosting companies offer domain name registration as a value added service to their customers? Do they need to have their own nameservers? How are different domains assigned to different accounts on the same server? If anyone can give me a rundown of how they do this, or how the webhosting community does this, I would really appreciate it.

all they have to do is run DNS and have a registrar they buy domain names from. Many integrate it with API. popular places to look are www.enom.com and www.directi.com.