Im in southern California and I let the plants die on the vines at the end of the year. Each line dies back at a different time - usually based on the ripening time of the plant. When the remains of the plant look sufficiently ugly, I cut them back to the ground. Over winter, rainfall and occasional watering should take care of the root stock.
After harvest, I use an out of the box 5-5-5 mixed into the top soil. If the plant has shown any hint of nutrient deficiency, I'll toss a fist full of bloodmeal and rock dust in as well. Past that, I usually wait for vegetative growth to see if anything else is needed in the soil.