This depends on the storage you use. For example, If you use ZFS, you can directly access the files on ZFS subvolume. Most other storage types use raw images, so you need to 'pct mount' that before you can access the content.
# pct mount <VMID>
You can then access the data at: /var/lib/lxc/<VMID>/rootfs
When you are done, simply do;
# pct unmount <VMID>