Johanna,
If you want to visually see the changes after you apply the css class, you must apply the same style sheet the page uses to the editor.
For example:
if the page uses three style sheets, you can apply them to the editor using the EditorWysiwygModeCss property.
<CE:Editor id="Editor1" EditorWysiwygModeCss="../first.css, second.css, /third.css" runat="server" ></CE:Editor>
>>The page where I've put the editor is linked to the Css-document from where I try to use the classes.
If you've already done that, please double check and make sure the style sheet path is correct.
If you still have problems, it would be really helpful if you could send us a sample aspx page which demonstrates the exact problem with more information.
Keep me posted.
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