On this site: http://doomed.ceruleandepths.com/indexx.php

When you move over the links (001, 002 etc.), and stay there like one second, a speech bubble appears and says "home" or "tagboard" etc.

How do I do that? What are the codes for it? Thanks for the help :)

those are link titles.
So you can use it like this

<a href="http://www.youURLhere" title="what you want it to read in the speech bubble">Click here for...</a>


You can also use it with pictures - just add a title.

As a side note, the website that you referenced achieved this affect using the alt attribute:
<a href="http://www.youURLhere" alt="Tool-tip text">Click here for...</a>
This is absolutely incorrect and should never be used to create a tool-tip. It only works in IE and should never have been implemented in that manner because the alt attribute is used to specify alternative text for images that cannot be loaded in a user's browser. Only the title attribute (as Zeraphine mentioned above) should be used to display a title in a tool-tip. Suprise, surpise, eh?

Thanks a lot for your help! I'll need it for my next layout and I'm sure it will look fancy :)