depends on which registrar you choose and which TLD you want.
Some registrars can do it in near realtime for some TLDs, some may require manual checking of contact information and stuff, some TLDs require all kinds of paperwork to be sent in (signed forms, sometimes birth certificates or chamber of commerce registration forms, etc.) which can take days or weeks.

This doesn't have anything to do with game development.

Try godaddy.com, I've been with them for awhile and you should have everything you need within 24 hours. The domain nearly instantly, but the name servers take time to update. Speaking of, I have to switch mine over to the new server.

Kind of an odd question given the advertising in your sig link.

http://www.hostingplex.com/r/12364
Hosting for $3.95, (yearly and bi-yearly plans)
300GB space
3000GB Transfers
Free domain on yearly plan
Unlimited ftp accs, mysql dtbs, subdomians etc


Signup took about 2 mins for me, just basic details and payment. Setup was almost instant.


I got my domain at fxdomains.com, the signup was kinda lengthy (6-8 mins) going through some pages with lots of offers. Domain was ready almost instantly after signup



So I guess you can have a domain and website in less than 15 mins these days.

I have been using godaddy for a few years now, for both hosting and domain registration, and have been very satisfied with their service. About once every 6 months they give me a call just to see if they can do anything for me and pitch any new discounts they offer. Makes me feel important...

The few Domains that I have reg'ed with them have taken an average of about 4-6 hours I suppose.

Well it depends on site buddy ...may b one day may be one year......