I agree with everything Vangogh has to say here . . . but maybe have 2 cents worth to add.
Typically, when a client wants a web site design, they want at the very least a template they can see in a browser. They may want more, such as design layering through regions of their web site, but they'll at least want a template they can use to keep building pages on their site one way or the other.
But I think you are also hinting at process.
Once you have a soilid idea of what the client is looking for in a design, the first step is to produce a (or a few) design creatives in a graphics application such as PhotoShop or Illustrator. This is just to work up design ideas and present them as an image of what the site might look like.
Once you've gone through a revision or few on the basic look of the site, then it's time to roll up sleeves and mark it up and lay it out -- that is break down the graphics into their component parts, write your XHTML markup, and pull it all together with your CSS. This phase too will probably require some revisions once the client sees it (it's rarely going to look just like the "picuture" presented in the creative phase).
That is, I'd expect that the client would be looking to you for both the artistic look of the site AND the markup/layout so they can see it AS a site.
From the way I read you, you're rather more in a "Project Manager" position. Maybe you can do one or the other of these, but clearly not both yet. So, you'll probably need to team up with someone who is an excellent graphic artist or a whiz as markup & layout, whichever one is not your strength.
And then there will be, inevitably, funcitonality issues on the site -- the site needs to DO something. Then you'll need a programmer adept at both client side (JavaScript/AJAX) funtionality and server side (PHP, ASP, .NET, JSP, CGI, etc.).
All of this said, my advise to you it to keep networking, just as you are doing here
