That is called a watermark. There are several sites on youtube that will walk you step by step through the process. It will be a matter of choosing the site/person that best suits your needs
It depends on how fancy you want to get. The simplest version can even be done with MS Paint. Just open a copy of the photo and type some text where you want it. You can select a font and colour. This was done with the MS Paint program that comes with Vista.