Hi, Blair!
It would appear that you are a candidate for:
Beginners html guide for DotNetNuke.
Basically, a link is formed with an "a" tag. You can see the HTML that makes up the content of a Text/HTML module if you click the "Source" button on the editor's toolbar. A hyperlink will appear something like this (I've added some spaces so that this will post as text and not be interpreted as a link):
< a href="http://somesite.com" >The Link < / a >
You would change this to:
< a href="http://somesite.com" style="text-decoration:none" >The Link < / a >
For you other question, you may want to change the "hover" or "visited" properties of the link. Hover is what happens when you mouse-over a link and before clicking it. It is probably better/easier to style the link and its hover and visited properties using CSS. If you Google around, you'll find some helpful HTML and CSS tutorials.