If I found designs for chinese characters on a website, do I need to get permission from the website to use them

That site apparently just shows the chinese text for "olympics" There is nothing unique about that, though you would not be able to make a use of it were it presented in some original or differnet way. Basic Chinese text is not copyrighted material. I am sure you could find the same text and other Chinese words on numerous government and public interest sites as well.

If the Chinese characters actually transliterate into the word 'OLYMPICS" then the super-trademark protection given to the International Olympics Committee will kick in to preclude your use of the mark on any commercial products sold in the United States. If you changed the Chinese characters so they no longer formed the recognizable word "OLYMPICS" then you would not have this problem. However, you would want to make sure what you change does not create a new translated word that some other trademark owner may find objectionable.

See the attached summary at the International Trademark Association website: http://www.inta.org/index.php?option=com_content&task=view&id=187&Itemid=59&getcontent=1

Stylized fonts are protected by copyright laws, such as the stretched "C" in the trademarked Coca Cola, however standard fonts are not protected and therefore you are free to use.