First step is to get Liferay set up w/ your database and to get your feet wet in it's use. Sounds like you've done that, so we can move on.
Assuming that you have a basic plan of what the site will include, your next steps will be actually making that happen. Create your pages. Add appropriate portlets. Adjust the security and permissions. Etc. Get it functioning how you want without paying too much attention to how it looks.
How it looks is based upon the theme you use. You can use one of the canned themes (classic), you can try one of the community themes (from the download page), or you can create your own theme using Eclipse and the plugin SDK.
Rather than looking at the site as a whole and asking "How do I build it", peel back the layers and take it one step at a time. Separate your concerns and approach them separately, and in the end you'll have your site and you'll realize that it was pretty easy to get from the canned system to your custom system.
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