The Box login screen has changed - but nothing else. They've just remodeled a bit.
If you haven't already set up Desktop Sync, go to the Cogwheel in the top right corner to see your settings, and choose "Get Box Sync."
Install this and when that process is complete, you should have a "Box Files" folder on your desktop.
Any folders or subfolders you sync to your desktop will be visible in the Box sync folder. See Pete if any questions.