DirectURL

Consider the following scenarios:

aria2 is running on a computer that is not locally accessible via the LAN and the files need to be copied from remote aria2 computer to the local computer
aria2 is running locally somewhere and setting up samba/nfs/etc is "meh"

HTTP to the rescue, already in the browser right?

Simplest way is to link your download folder or use python to setup an extra http server.

Steps using linked download folder

as part of configuring aria2 to make life easier you will have set the global dir option to something like /home/aria2/downloads
clearly this folder is owned by the user aria2
open a shell session logged in as aria2
run ln -s /home/aria2/downloads /var/www/aria2/downloads
go to webui-aria2 in your browser (http://serverip:81 - assuming webui-aria2 is running on port 81)
go to Settings > Connection Settings
scroll down to Direct Download and put http://serverip:81/downloads/ in base URL field (make sure have the / on the end)
now that URL has been specified all the files will be converted into clickable links
checkout the more info on a download and see for yourself
if you click on files that aren't finished downloading you're going to have a bad day

as part of configuring aria2 to make life easier you will have set the global dir option to something like /home/aria2/downloads
clearly this folder is owned by the user aria2
open a shell session logged in as aria2
run cd /home/aria2/downloads
run python -m SimpleHTTPServer 8080
webserver is now running on port 8080 and will serve files from the directory the command was run in
to test open up http://serverip:8080 - should get a directory listing. any browser errors and something hasn't been done properly, check IP/PORT etc
go back to webui-aria2
go to Settings > Connection Settings
scroll down to Direct Download and put http://serverip:8080/ in base URL field (make sure have the / on the end)
now that URL has been specified all the files will be converted into clickable links
checkout the more info on a download and see for yourself
if you click on files that aren't finished downloading you're going to have a bad day