[This is a Wiki post, feel free to edit.]
Most information here comes from the ownCloud user manual, which shows many other ways to connect, in particular from other OSs.
Mounting your Box folder under Linux
On a BIC workstation, most of the work can be done by running this convenient script:
sudo install-WebDAV.sh
Then edit the file ~/.davfs2/secrets and add a line at the end:
https://box.bic.mni.mcgill.ca/remote.php/webdav <username>
Replace <username> by your McGill email (not your BIC account). Note that some users have email aliases, but only the “base” McGill email will work to log in to box.bic.
You need to logout and login again on the workstation to activate the required group membership to davfs2.
Then manually mount or un-mount at the command line with:
mount /mnt/webdav/<username>
umount /mnt/webdav/<username>
You will need to enter your McGill (not BIC account) password when mounting.
Warning: ~/.davfs2/cache will quickly grow and fill your home folder quota. It should therefore be linked to somewhere local. See this post.