Our customer wants to use Joomla! and I have no prior experience of it. I have been looking thru Joomla! documentation and tutorials over net, but I just cannot find how can I make just static html pages and menu. Joomla! adds some tables (for layout!) in your articles and it of course will ruin my own html.
You can add custom html by going site's administration panel and from there go to Extensions-Module Manager, on this page click New button on top right side and from next page select "Custom HTML"
Joomla has a steep learning curb if you're not serious about learning it. If all you're doing is static HTML pages, using a different CMS might be the answer. Perhaps you need to ask your customer why they want to use Joomla. If they reply that it's shiny, then you need to persuade them to look at all the other options. It won't help either them or you if Joomla turns out to be the wrong CMS.
Few thoughts on your question:
I'm going to assume your using the standard JA Purity template here.
Joomla handles menus for you. You do not have to have the menus going down the left or right side as modules if you don't want to. You can configure a horizontal menu which appears just below the header. Look at the Customizing the JA Purity template tutorial for the names of the different positions available. You change the position and the type (vertical to horizontal) in the Module Manager. The positions available for menu positions are limited by the template you use.
You mention just having static HTML pages. So in Joomla you will treat each page as an article. Create a new article for each of your pages. You don't have to use the standard editor if you don't want to, you can toggle to HTML mode or turn it off completely.
You will need to build up a menu structure using the Menu manager. Each menu item can be assigned to show a single article layout, and you can select the correct article to show at that point.
If you just want a header, a body containing the article, and a footer, then just make sure you have turned off all any other modules such as the login on the Module Manager. Your article will span the width of the page then.
The template has a footer. You can add what ever you want in there. This is where the Custom HTML module might come in handy. You can create a module and then place it in one of the template positions available in the footer.