There's an easy way out of all this.
Do you have a registered domain name? If you have, do you know where it's hosted?
If you do not have a domain name you can easily register one (and set up a hosting package) yourself - you don't need the designer to do this for you.
I recommend Heart Internet because I use them extensively myself, and have found their service to be second-to-none. Once you have your account with them you can send the login details to your designer - that's all he will need to upload your site and get it working.
Just go to
click here and click on the hosting link (the maroon coloured one). Now select your package - I recommend the starter package if your site is fairly new - and away you go.
If you get stuck come back to this thread, and we'll sort it out.