Batch uploading files
If you are comfortable using the WebDAV protocol to copy files, you can follow the instructions for Uploading multiple files using WebDAV.
A quicker, potentially easier option is to use the Content Editor's built-in importer.
This feature, normally used for importing an exported site from Roxen CMS, also works great with files from your desktop. You compress your files into a ZIP (.zip) archive, import the archive into the Content Editor, and the importer automatically explodes the files into your chosen directory, retaining any file hierarchy.
Creating the .zip archive
The import feature only works with .zip archives. Both OS X and Windows 7 or newer have built-in graphical interfaces and command-line interfaces for creating .zip archives. If you want to upload the parent folder for your files, you should include that in your archive. For this example, we will instead navigate inside the folder full of files to begin.
Select all files inside your target folder. Right-click (control-click) one of the selected files and choose the Compress # items menu option. This will retain the original items in the Finder and create a new file named "Archive.zip" inside the same folder. You do not need to rename this file.
Select all files inside your target folder. Right-click one of the selected files and choose Send to → Compressed (zipped) folder. This will retain the original items and (inside the same folder) create a .zip file based on the name of one of the original files. You do not need to rename this file.
File → Import…
From the right side of the Content Editor admin interface, select the File → Import… option. Then click the Upload archive in ZIP format… link and use the Choose File button to select the archive you just created. Click the Upload & Refresh button.
Make sure you select the checkbox for Filter invalid filenames from import, especially if you are on OS X. Otherwise, your import will fail as soon as it hits an invisible file or a "dot-underscore" file.
After clicking the Next button, you will have a chance to preview the path of the new files. If they are not going to be imported into your desired folder, cancel and try again. Otherwise, click OK. Then after your import is complete, you can batch commit your files via the Versions → Commit… option on the left side of the admin interface.