Could you please give links to where you got these images from? Your wording is vague to the point that there are several different solutions depending on exactly what you mean. That said, I will present some of the more common methods.
Regarding the link colors, you can change the color of an individual link if you use source mode. The wiki may just be doing it manually for each link. In source mode, it would look something like this.
[[PageName|<span style="color: displaycolor;">DisplayText</span>]]
Another option that would do it for all links to a specific page automatically would be to use wiki CSS. Only admins can edit the wiki CSS but depending on the specifics, it could be something like this.
a[href$="/PageName"] {
color: displaycolor;
}
As for the content on hover, it could either be the HTML title attribute or some sort of tooltip script. If it is just basic text, then using the title attribute will do. Here is an example. Again, source mode is needed for this.
<span title="This shows on hover.">Hover over this text for more.</span>
For an image, it could just be the caption. If you are inserting the image using visual mode, I believe the insert interface has a field for this. If you are using source mode, then it would look something like this.
[[File:FileName.ext|This shows on hover.]]