You install bind9 on your server, which i'll say has the IP address 126.96.36.199; we'll call it ns1.domainname1.com. You configure it to be primary for the three zones domainname1.com, domainname2.net and domainname3.org (let's spread the love in the TLDs!). Ensure that you have an SOA record that lists ns1.domainname1.com and ns2.domainname1.com as authoritative for each domain, and A records for both ns1.domainname1.com and ns2.domainname1.com pointing to 188.8.131.52).
You test that they're working by
ns1% dig soa domainname1.com @localhost
and likewise for the other two domains. Don't go any further until you've got this bit working.
Change your glue records, that is, the records maintained through your registrar (the organisation you pay for the right to have the domain names domainname1.com, domanname2.net, etc.) so that the listed nameservers for each of the domains are ns1.domainname1.com and ns2.domainname1.com. When doing this for domainname1.com's records, you will have to give the IP addresses of the two nameservers as well, which are 184.108.40.206. This avoids the chicken-and-egg problem where I go to look up www.foo.com, get told that the authoritative servers for foo.com are ns1.foo.com and ns2.foo.com, so I try to look those up, and get told that the authoritative servers for foo.com are ns1.foo.com and ns2.foo.com, so I try to look those up, you can see where this is going wrong, yes?
And that should be it. You can check the glue records are right with
and you already know that your nameservers are serving because you checked it with dig above, right? Check it again anyway, preferably from a third box so you don't overlook any firewall-related or i-only-listen-on-127.0.0.1 issues.
Optional extra: find a friend with a nameserver and have him/her run secondary NS for you. Generally, you need to advertise two NS records for a domain, and while it's possible to list the same one twice, it's bad form. There is a bunch of other stuff you need to do here, making sure that ns1 allows your friend's box to transfer the zone, that your friend's box is configured to look to you as master, that sort of thing). If you do all this, change the A record for ns2.domainname1.com to your friend's name server's address in your zone files, and your glue records accordingly.
Enjoy nameservery goodness, and have a well-earned coffee. Does that make sense?