The problem with your button is that you set its position as absolute. That means it stays in the same spot no matter what happens. Because of that you need to define its position in relation to other elements.
For getting the “read more” button on top of the picture, set the Robin Williams picture as a background on the “thumbnail” div. Once you do that you can put the button inside the “thumbnail” div and adjust its position there.
To keep the text underneath the picture make it into its own div and adjust margin so you get it right underneath the image.
Here’s a fork I made from your page to demonstrate. This does create some new problems though on different screen sizes. I would suggest some media queries as a solution so you can keep the Robin Williams picture at an optimal size.