Download from the project page
You can download any public project from the project page using the "Download All Files" button:
This will download the files as a ZIP archive. You'll have to extract the files from the archive before loading them onto a USB drive to take to Origin.
Download them from your account
If you already have the files in your account, via syncing or uploading them, you can access the files in Origin Files:
From the Origin Files view, you can download individual files, but not entire folders. Hover over a file with your mouse and click Download
Once you've downloaded your files, you'll need to move them onto a USB drive formatted to FAT32, plug it into Origin, and access your files via the Import tile on Origin.