I created a template with Artisteer. I'm not quite sure if I should just copy paste the whole template.css file which Artisteer created for me into the styles.css file or just the part with the unusual fonts. Anyway it does'nt seem to work both ways. Could you please tell me what I am doing wrong, because I really would like to use your great solution.

This is my website: test.bernartwebdesign.nl

I would like to use the font mackan.ttf in the mainmenu above and in the headings.

I attached my template.css

No you should not copy the whole template file into the styles that will look really funny.

If you know basic css, to get the heading you read what the html output is.

In you case:
<h2 class="art-PostHeader">Welkom</h2>

and to change it add this line to styles.css:
h2.art-PostHeader {
font-family: mackan;
font-size: 19pt;
color: #fff;
}

And the heading is done.

Same goes for the menu. You need to know how css works. And im not a teacher for that. I can show you the basics but google does the rest.