Is there a simpler 'export to html' function?

I am searching for a much simpler export-to-html function, so that:

Hello, this is an example of some formatted text that wants to be transformed to the html way.

becomes:

Hello, this is an <b>example</b> of some <i>formatted text</i> that wants to be transformed to the <a href=“http://en.wikipedia.org/wiki/HTML”>html</a> way.

The result could replace the original text or it could show up in a new window.
In a document only marked text should be operated.
Basic styles like bold, italic, underlined and Hyperlink would be sufficient for me.

I guess, this needs to be programmed (makros), but I don’t have any clue how to do that. Is there anybody, who can give me a hint?

Welcome to Ask.LibreOffice. I do not know of any extension to do that, but you could learn to create a macro. Search around the internet for tutorials and examples. For example, look at http://stackoverflow.com/questions/tagged/libreoffice+macros and http://stackoverflow.com/questions/tagged/openoffice.org+macros

Have you tried in Menu/File/Export?, one the options is xhtml.

The XHTML format makes use of <span> elements rather than direct encoding/styling using <b> or <strong>.

Of course I tried Menu/File/Export - but this is just my point: This function is creating a too complex code that is simply unhandy.

This lengthy and detailed thread on character styles is related to your question. The remarks in that thread by @CyanCG are especially worth reading as they indicate the problem with obtaining a more simple form of HTML markup.

The short answer is that there is no current method of achieving what you require (as @carnendil indicates). LO makes extensive use of the <span> element rather than <i> or <b> (or the recommended <emphasis> and <strong>) elements. The <a> element is not such an issue.