When you visit the Canadian Liberal Party's website (www.liberal.ca) they have a "What's New?" section on the homepage. The black text there can't be selected by cursor or copied because it's in an image, but can be checked by the Ctrl+F function. How do they do that?

I don't think I understand your question. After visiting the site, I tried copying, pasting, the "What's New" text and several other text (paragraphs, etc.)
It isn't an image. Basically in a web site, you can have an image, or text, and tie a hyperlink to them (that's without getting into the advanced "flash" graphics.
If you hold the mouse button, (typically the left button) and drag it across the text, you can select it, then unless there are copyright settings in the site, you can copy it.

Also, images can be hidden behind blank GIF files. The GIF file is a place holder and can be put up on top or underneath the image. In the "good old days" FF had an add-on called "Background image saver", which would remove the GIF overlay, and download the image under it. This hasn't worked with any recent version of FF.

In some websites, there is a script blocking right click functionality, thereby preventing downloading images, "No Script" takes care of that.

Blocked images can also be accessed through, "tools" >> "page info" >> "media".

But who would do such a thing, certainly not I.

Its not an image, a JavaScript was placed on that bit of text to it wont be copied when someone decided to write an article on it. The script simply does not allow the test to be selected. Its gone now anyways...