If you can access your remote computer through ssh (I personally use putty), you can upload your data to galaxy through the FTP function. Simply navigate to the remote directory that contains the files that you want to upload, then type
ftp usegalaxy.org
You will be prompted to input your account and passwords (notice that your account is your email address that was used to register, not your galaxy login name).
Once you are logged in successfully, you can upload your files. Type:
put [path/file name]
Then on usegalaxy.org main interface you can retrieve your data via normal FTP method (Upload data from your computer => Choose FTP files).
Good luck!
You can have Galaxy download the data for you from a public url. Watch this video to learn how to do it: https://vimeo.com/120973708