Hopefully this is working now! 
We have another method for those who prefer to work on the command line. And @igor is correct – this all works about the same for someone moving data up from their own computer. The limit is usually the internet speed of the computer where the data is coming from.
Most UseGalaxy.* servers now support the galaxy-upload tool as far as I know. It works through the API and the script is local to your computer.
Loading data up to a 3rd party cloud source then moving it over to a public Galaxy server from there, then the archive result sent back to your cloud storage, is another really nice choice if you want to only have to *get the data up into the cloud" one time or expect to have really large results. Galaxy archives are just compressed directories, and can be navigated to pick out individual files if the 3rd party service supports uncompression from tza. (On your own computer this is always possible, but maybe not at all cloud storage providers).
What connections are supported differ by server. Check under your account User > Preferences to see the currently available options. Some are under Manage Information and others might be in the other views linked on that top level view.