Assuming your BB10 OS version has it, I would go to system settings, storage and access, access using Wifi, and set the password. Then, on your Linux box, you can use smbclient to list the available shares (one for device memory, and one for media card). Use mount with cifs filesystem type to mount each share. Finally, copy the files from the mounted filesystems.
Alternatively, you could go to settings > storage and access > access using USB, and make sure USB Mass Storage mode is turned on. Once connected with a USB cable, your Linux machine should see the phone and mount the device and card like USB drives.
If it does not detect the device and mount it automatically, you might be running a very simple desktop lacking good auto-mounting support, in which case your first steps are to learn how to use the fdisk, mount, and umount commands.
