As others have said, a simple right click in a regular Finder window will make it possible to "show package contents".
For a file open dialog, use the "Go to location" functionality (⌘ Cmd+⇧ Shift+G) and type the full path to a subfolder or subfile of the package. For example...
/Applications/Skype.app/Contents
After doing that, you can browse around inside the folder normally.
