Let's say download directory is /home/username/downloads.
usermod -a -G debian-transmission username
where username is your username. with this command you are being added to debian-transmission group.
chmod 0770 /home/username/downloads -R
this will set the owner and the group users to read/write/execute on this folder.
chgrp debian-transmission /home/username/downloads -R
chgrp will change recursively the content of download folder to group "debian-transmission"
Tutorial taken from ubuntu-for-humans.blogspot.com