In the main Empathy window, right-click the contact that you want to send a file to and click Send file.

Select the file that you want to send and click Send. The File transfers window will appear. Wait for your contact to accept the file transfer, or press Stop to stop the transfer from happening.

If your contact accepts the file transfer, you can watch the progress of the transfer and see the estimated amount of time remaining before it is complete. If they do not accept it, the status of the transfer will change to File transfer cancelled and the file will not be sent.

Once a transfer is finished, you can just close the File transfers window. If you have lots of finished transfers listed in the window, click Clear to clear the list. This will only remove the files from the list and will not delete them from your computer.