NICs on a virtualization box

[techlists at phpcoderusa.com]

Hi,
I'm wondering how VPS servers are configured.  I have a VPS with a 
dedicated IP.  I assume I share a box that has a number of virtual 
machines and I assume each VPS has a dedicated IP.

This is a hardware question.  I assume the box has at least 2 network 
cards.  So lets say the server has 20 VPS on it and each has a dedicated 
IP. Does the box need a NIC for each IP or does the box have NIC cards 
that can service/route multiple IPs?

I have a Dell consumer grade mini tower computer with a single NIC which 
is built into the motherboard.  I assume that NIC can only service one 
IP address, is that correct or can I install virtualization software on 
this computer and use the NIC for multiple IP's?

Did I just open a can of worms?

Thanks in advance for your wisdom.