Digital photography

How do I go about it? Copyrighting that is.

As Well_is_it said you do own the copyright as you're the one who took the picture.

I would just make clear to viewers that it is indeed copyrighted (and not open source or under one of the creative commons licenses - which are worth looking into by the way).

To do that you'd mark them as copyrighted in the first place (like you do on flickr by default), or add a line like © Your Name, all rights reserved.
Plus set your camera / scanner to put your name in the files' EXIF data automatically, or do this afterwards (File > File Info in Photoshop).
This info usually stays within the file even when it is renamed / resized / uploaded somewhere else.