I just signed up for a VPS account and have never had one before.
My domain is with godaddy and VPS hosting with another provider.
My question is how do I set the nameservers if the VPS provider does not provide this info?
Either you a) use GoDaddy's nameservers and modify the A-records to point to your new VPS where you will host your site, b) run your own nameserver on your VPS and change your domain to use them (easiest when done with a control panel?), or c) check with your provider if they provide managed nameservers and take it from there.