You can drag-and-drop one or multiple media files from your local file browser to anywhere in Console window to upload them.
Browse for files
If you would like to browse your computer for files to upload instead just press the "Upload" button in the top right corner of Console and then click somewhere in the grey box "Click or drag-and-drop files to upload." and you will be prompted to select files.
If you're browsing the Console in a small window such the web browser on a mobile device you will see an upload icon instead of the "Upload" button, pressing this icon will bring up the file selector right away.