Hi Peter,
That's a good Q and easy to fix.
There are a couple of ways -
If you want to remove border just for this image go into your WYSIWYG editor and click on the image - you should see some properties and a border property - make the border 0.
To change this in the template so that it never happens you can add this rule to your template.css
img {
border:0px;
}
You can put that in anywhere on its own line.
Another tip if you have not done this already is to install an improved editor - I really like
www.joomlafckeditor.com/
And they have a free version.
It makes image management easier too.