Finally fitted the passenger side mat - and got some better photos of the process this time:
The necessary holes in the carpet are already part-cut. First you need to cut and remove two small squares and finish the part cut of each flap:

Each mat is secured by two plastic clips - here they are before fitting:

Having made the cuts, you slide the serrated part through the flap:

...and then snap it shut:

This shot shows both clips in place:

Finally the two holes in the mat clip over the posts in the plastic clips:

Once done, there's no way those mats are going to slip. Photos above hosted on
my Flickr account.