How does a DNS resolver work?

I've been looking on the internet how DNS work but so far I have only found explanations that are very superficial about it.

What I understand so far is that there 13 root servers. First you make a request to your DNS server, if its in cache it will reply with the IP, if not then they send the request to a root server, they will reply to look at an authorative Top domain DNS server (Let's say .com) and then those servers will reply to look at the nameserver DNS, which will return an IP if it exists.

From my understanding this are 3 layers. You got your root servers, top domain servers and the nameserver. An average user who owns a website will be able to control the nameserver and the registrar which links your domain name to a nameserver of your choice.

My question is how does a DNS resolver work. Like Google have their own DNS (8.8.8.8 and 4.4.4.4) but how do they set it up so they can query root servers, then top domain name server and finally the name server. Can an average user have their own DNS resolver? Or you need to be some sort of business or ISP to do it?