The dog one you get from a dog barking at a fridge, I believe.
Not sure about the cat, but I think it is from them being started?
Vampire gnome you get from growing plasma fruit bushes on your lot.
The witch one likes to sneak into your sims inventories when they go through the haunted house.
I think you can get the Winter one from building snowmen/igloos.
And the Spring one from searching for Easter eggs.
The caveman you can get from traveling to the past in the time machine.
The diving one, I'd assume you'd get from diving, but my sims got it just from living on a houseboat.
The inventing one you get through inventing.
Those are some off the top of my head, though I have not had my coffee yet this morning...
If I remember correctly, I think Carl's site may have a guide or something for the gnomes.