I'm not sure which is more usual. My guess is that most people have their hosting provider handle DNS, though I know that my registrar will do it for no extra charge. I can tell you how to figure it out, though.
The following directions assume you have access to a Unix-style command line on a machine connected to the internet. There are Windows tools to do this as well, and web sites that will let you read 'whois' information, but frankly I don't use them so I don't know exactly which packages to recommend. I'm sure someone here can fill in that blank, though.
All the information about your domain is stored in the Whois and Domain Name systems. To find out who the contact people and primary name servers are for your domain, simply type 'whois mydomain.com' at a Unix-style command prompt. At the very least, you will get a response like the following:
Whois Server Version 1.3
Domain names in the .com, .net, and .org domains can now be registered
with many different competing registrars. Go to [internic.net...]
for detailed information.
Domain Name: MYDOMAIN.ORG
Whois Server: whois.myregistrar.net
Referral URL: [myregistrar.net...]
Name Server: NS.MYDOMAIN.ORG
Name Server: NS2.MYDOMAIN.ORG
Updated Date: 24-may-2002
>>> Last update of whois database: Fri, 25 Oct 2002 04:58:23 EDT <<<
The Registry database contains ONLY .COM, .NET, .ORG, .EDU domains and
There may be more information after that, depending on how recent a version of 'whois' is installed on the machine in question. What we see here is enough to let you know that I handle my own DNS. If the 'Name Server:' lines pointed to 'NS.MYREGISTRAR.NET' and 'NS6.MYREGISTRAR.NET', you would know that my registrar was hosting my DNS service. Likewise, if they were 'NS.MYHOSTINGPROVIDER.COM', you could conclude that my DNS hosting was provided by my web hosting provider.
Those names are all examples. Nothing requires that name servers be named ns#.domain.tld, it's just a common convention. The domain that the servers belong to, though, will tell you who provides the DNS service.
<added>OK, as I should have guessed, 'myregistrar.net' exists and is owned by a registrar. Silly me. It's not the one I use and I did not mean to endorse any particular service. If you want to know who I use & like, look in my profile and then look up my domain ;)</added>