Every time I let mine (Lillian) off the leash she goes after every varmint she sees. Our yard is know by the neighbors as "Lily's Land". I have not purposely taken her hunting but my brother-in-law's JR drags in groundhogs once in awhile.
My old boss' jack russell would bring home black snakes, chipmunks, squirrels, deer were too big to carry but still susceptible to being chased through the yard. I have seen them chase and "corner" hogs.
I would imagine it would be very much the same as training any other dog, particularly a beagle or hound.
I recently read that Jack Russel's were originally bred for hunting, and take to it very well, particularly birds, as they can get to brush and cover that alot of retrievers probably can't. One of the books I'm reading - "Dancers in the Sunset: the Musings of a Bird Hunter", has a chapter devoted to his Jack Russell Terrier.
Years ago my neighbor had a Jack Russell, one tough little dog let me tell ya. That dog would go right down into a grounhog hole, and more often than not you'd hear the sounds of snapping teeth and growling. Soon enough he would be backing out the hole with groundhog in tow. Once they both were on open flat ground the real fight was on. Sometimes Jack won sometimes not and the hog made off to other parts. If he got hold of the groundhog by the throat or the back of the neck, it was a done deal, dead pig, but groundhogs are some tough critters also. Fight like a Badger. Somedays I'd see him bringing a dead hog home thru the back field. The dogs ears and face would be all tore up and bleeding, talk about a gutsy dog. Then one day, I guess he was 10 years old or so, he laid down in my neighbors yard under a apple tree, went to sleep and never woke up. All those years of fighting and guarding the property must have taken it's toll on old Jack. Even though he wern't my dog, I miss the old boy. T