The j hooks are placed onto the top rail of the rack, the s hook or ring on the elastic cord is pulled down and hooked to the rack leg/strut near where the rack mounts to the bike near the dropout.*

You might look into getting a replacement kit from Arkel or Ortlieb as way of upgrading that mounting system.

*I have the same mounting hardware on some old Nashbar Townie baskets- and a hard enough bump or heel strike can cause the bag to bounce off the rack.