You could run separate subwebs off your one IP, but if you want to run multiple domains you really need to contact your ISP to get additional IP's assigned. As for the DNS, it's probably a bit more than we could get into here. If you go into Windows Admin Tools>DNS>Help>Help Topics, it gives you pretty good step by step instructions though.
Good luck and keep those hosting service url's handy though. You could still host websites on a virtual server somewhere, and bill your customer directly too. Many hosts have a sort of 'reseller' program where you can make a few bucks (or quid

) that way. Sometimes that's easier and a lot less hassle, especially if you're only running a couple of sites.
All the best,
E3