If you're looking to download something from the internet, there's no need to download it to your local machine first, then upload it (which is what I would have done before I found out about this). You can use wget. If I wanted to get WordPress, I'd do the following command:

wget http://wordpress.org/latest.tar.gz

That will download WordPress to your current folder. If you want it somewhere else, you can use the -P switch, like so.

wget -P "/home/shamess/downloads/" http://wordpress.org/latest.tar.gz

You can also log into an FTP server, or any HTTP directories that need authentication, using --user and –password. Which is what I should have done when I was transferring files from my old server to this one.