How can I select an area of an image then paint with that area in Photoshop?

Use the pen tool to trace the area of an image that you want to select. When you're done, use the command "Ctrl+Alt+Enter", and it will select the image.

Then you can use your paint tool to paint the area. Or if you want to just fill out the area with a color, just set the color in either your BG/FG, then use the command "Ctrl+Backspace" for BG color and "Alt+Backspace" for FG color.