This will be an oversimplified description, but you'll get the idea. Think of the DHCP server as the phone company and the DNS server as a phone book (hopefully, you're old enough to get this. ;-) ) When you connect to a network, the DHCP server will give you a dynamic IP address from a pool of addresses that it controls. (A DHCP server can be something that controls a large network like the campus network, or something as small as a router in a home network that also serves as a DHCP server. I'll skip the explanation of the 192.168.. address pool. You can google that one.) This address may or may not be the same each time you connect, thus the dynamic aspect, but it does need to be unique on the network.
By contrast, there are also also static addresses, which are normally set permanently on a computer, and usually manually assigned by a network administrator from a pool, but nevertheless, unique on the network.
The DNS server, on the other hand, serves a different purpose. When you want to connect to something like google.com, your computer sends a request to the DNS server, "Give me the IP address for google.com". It responds with the data your browser needs to connect.
But, how do you find the DNS server? There are actually many DNS servers. In this case, one is maintained by Yale, and the Yale DHCP server will tell your computer where the DNS server is.
So how does the DNS server get all the global data for URLs and IP addresses? The DNS system is a big tree of servers - local servers, regional servers, and then a handful at the top of the pyramid that control the names and IP addresses for all of the major domains, .com, .net, etc. When your computer requests a lookup, your DNS server checks to see if it knows. (Not every URL is stored on every DNS server.) If not, it goes to a higher level DNS server to find it, on demand. It will then keep it in cache for the next request. (Similarly, when a site changes their IP address, or come online for the first time, that data starts at the top level and is propogated downhill through the network over time. This process can take a couple days to get everywhere.)
Anyways, that's a simplified description. If I've made any errors, I'm sure someone will correct it. ;-)