Where to find gene manipulation video (or photos)
From the comment section:

We don't have to see the actual changes. It's like chemists who will mix compounds together and obtain a new molecule. They dont see the chemical reaction per se but can test the new molecule to make sure what they predicted would happen had happened. Finally we often use fluorescent proteins to track some of the modification performed (which could involve a microscope). For the how, well that's a bit broad and involves too many notions to make a summary here.