First you need to find a nice template that you like. There are many free WordPress template sites. It is very easy to find Go to Google or any favorite search engine and do a search for "Free WordPress Templates" or "Free WordPress Themes".
Static WordPress site rarely need the blog items like calendars or archives etc. A simple solution is to navigate in your WordPress administration panel to design> widgets. You can then add or subtract the widgets you want and you can make the sidebar look exactly as you like. This way you do not have to touch any code.
Now for the plugins. I recommend these basic plugins .:
Add the all in one seo plugin.
Add a sitemap plugin if you want. This is very good for search engines to find all your content.
Add a Google Sitemap and register it at Google. This is very important and will help you do well in Google.
If you want AdSense or affiliate banners add the ads manager plugin or any of the other WordPress plugins available. I like and use ads manager. It is very versatile and it can also be used to easily add other types of banners to a page and control it by the Admin panel. With ad manager you also need the exec php plugin. This is really important this if you are going to hard code includes into the template. I use it to add banners to the sidebar via widgets and the text widget. If you do not know what this means then you can forget it.
Find the plugins at WordPress.org or do a Google search for each of the above plugins. If I am looking for some type of plugin I usually do a Google search by "keyword" and then "WordPress plugin." I always navigate to the authors site for the latest plugin and instructions on how to use the plugin.
Activate the plugins in your WordPress admin panel. They are located in the plugins link to the right if you are using WordPress 2.5. Again, I recommend that you read the instructions that are on the individual author plugin sites as to how to use each WordPress plugin.
Create a page. Label it whatever you like. Scroll down the page writing panel to the "all in one seo" area and add keywords and description to your page. This is the same as adding the keywords and descriptions to the meta content in the head portion of your template.
Scroll down some comments and pings and turn off "Allow Comments" so you will not see a user comment box. I want my site to look like a static site so I do not need commenting. If you also want un-check Allow Pings. It is up to you. I always un-check both.
At the bottom of the page you will see a "page order" area. If you want to have a certain order to your pages in your category menu then name the page you want on top of the menu 1 then the next page you create 2 etc. You can later change the order of your pages by using this feature. This is good so that maybe a sales page will be on top.
I also tend to use the subcategories Parent - child a lot. As an example, I will make a page called "articles" and then add different article pages as a subcategory to articles. I then add some form of introduction to the main article page and have the other articles easily accessible off the main article page. A nice touch for me is that I like to find a template that has a horizontal menu bar with drop down lists. I think it looks very classy. For me everything is then neat and orderly. But this technique is up to you.
In the WordPress admin panel go to settings> reading. On top you will see reading settings. Then "front page displays". In the front page displays the radio button "A static page (select below)" and then from the front page drop down menu click the page you want to use for your front page. That page I usually title Welcome or I will add a keyword rich title. If you do not want any title leave blank.
With just those little changes you have the start of a static website with WordPress. The key is to use pages instead of posts, add keywords and descriptions via the "all in one seo" and your site is a really nice static website. Remember you can control the way the sidebar looks with widgets.
Do not choose templates that make use of the WordPress tagging feature initially. Some of these templates are called newspaper themes. They are a little harder to do and take a little more to understand. Once you master the basic look then you can branch out and try the tagging features of WordPress.
You can add to this basic formula to make your site even more user-friendly. Again, the above tips will give you a basic static and great looking website.