I'm trying to understand what it takes to register a domain.
Domain registrars vary in their prices. There has to be some baseline cost to a registrar, on top of which they add their markup.
What is that baseline price? Is there a way to register a domain on your own without going through a registrar?
There is a non-profit in Los Angeles called ICANN with a department called IANA, and this non-profit gives several companies special monopolies on selling "top-level domains" -- those companies are, in principle, "domain name registrars". So, for example, I have the domain drostie.org; this is in the .org top-level domain, which is maintained by the Public Interest Registry.
When you want to look up "drostie.org", your computer first looks up the ICANN servers and asks, "who's responsible for .org?" and it gives a server at PIR. It then asks the PIR server, "who's responsible for drostie.org?" and it gives my web host's IP address.
So ICANN does not need to know directly, but PIR's computers needs to know. Here is where the registry steps in: PIR does not deal with you directly, but through a middleman. The middleman allows you to manage your .org domains through the same interface as your .com domains even though these are managed by different companies with different back-ends; it also in some sense reduces the sheer number of clients and transactions which PIR needs to engage in.
Thus in a strict philosophical sense you cannot avoid "going through a registrar" because in some sense PIR is a registrar -- "registry" is right in the title, even. You could try, if you were enough of a company, to do direct business with PIR, but that might set you up for numerous headaches if all you want is a working domain.
Typical prices are generally less than $15/year for a domain purchased through normal channels; Gandi and NameCheap are two popular registrars which people are usually happy with; GoDaddy is popular but has a bad reputation generally. A couple of those dollars go to ICANN, a couple go to PIR, and the rest goes to the middleman.