In the back of these photos, you can see the start box (the green outlined thing). It has mesh on the front of the doors, so the dogs can see the lure and be ready to break out of the box when it opens.
Over jumps is the same, except jumps made out of cloth covered foam are added. The jumps are soft so that if a dog hits them, they won't get injured.
For both over jumps and on flat, the dogs end going through a padded wall that has a small hole in it, big enough for one dog to fit through. First dog through the hole wins. Since this is terriers, sometimes there can be disagreements about the entire process. Because of that, dogs are required to run wearing muzzles.
Like the rat games, terrier racing is a fun sport to do with a jack russell, and most of them naturally take to it (though training on box loading can be pretty important for many dogs).