Simply drag and drop the file(s) from your system folder to the media database. The upload process will start automatically. The progress bar on the upper right indicates how much of the process has been completed.
If you have selected multiple files to upload, and only wish to remove single ones, you can open an overview of your files with the arrow on the right, next to the progress bar, and remove individual files here.
To cancel the entire upload, click the cross on the right side of the bar.