All you have to do is go to the photo you'd like to add people to and click and drag a box around the individual's face. A box will pop up, asking if you'd like this to be a note or a person. When you select 'person,' a box pops up and you can type in the person's name. It will search for user names or real name from your contact list. You can now view all photos of a tagged contact.
There's the drawback: the only people that you can add are people that you have marked as contacts on flickr. So, your mom doesn't have flickr? Can't mark her. All of the ancestors in my photos? Can't mark them. This is a major drawback to this great new feature, and I'm not sure why flickr has designed it this way. On Facebook, you can add a name regardless. I hope that flickr will adjust their People feature to be more flexible - I'd love to be able to add 'people' to all my genealogy photos.