EDIT: Misread your post. Yes, using microsoft paint or whatever default image editing software your computer comes with, you could easily add text to your photos before you upload them. It'd be time consuming and the finished product won't look that great.
You say "own," though, in reference to "photo editing software." There is a good deal of free programs out there that will allow you to easily make the vast majority of edits most photographers would want to make to their photos- cropping, adjusting contrast/color levels, etc. Most of these editing programs also have an option to easily add a watermark, which can say whatever you want it to.
Picasa, which is owned by Google, is one such program.
Windows live photo gallery, if you have a computer with windows, is another. I'm sure there are plenty of others out there.
In the same vein, many image-hosting websites (like picasaweb) allow you to customize and state what rights you reserve for your photos on the web, using the various options available under creative commons.
I would caution you, however- adding a watermark to your photo doesn't actually provide any greater level of protection from someone misusing your photo without your consent. It's easy to crop out copyrights, and those with a greater level of skill in image manipulation can even photoshop them out. You can make watermarks super intrusive so that it's impossible to edit them out without destroying the image, but then people will derive less pleasure from viewing your photo.
The reason most professional photographers use watermarks is not for copyright protection, but so that if someone finds their photo on a 3rd party website, that person can easily find the photographer and be exposed to the photographers other works of art. The reason most amateur photographers use watermarks is because they like to pretend that they are professional photographers and like to think that someone would actually steal their photos.
That's not to say that it hasn't happened- not too long ago a bunch of photos and trip reports were taken from another northeast hiking message board and posted elsewhere without the consent of the photographers/authors.
