Should I pull everything? Cover with a tarp? Mulch? Leave exposed? Should a rake the leaves from it or leave them? Any other winter preparations I should make to make spring that much easier on it?
Choose your garlic patch and plant it now. Mulch that. Straw is ideal if you have it, shredded leaves are OK, whole leaves mat down a bit too much, and also blow around too much before they mat down.
If you have carrots, kale, or other crops that do well in the cold, leave them be - mulch and mark the carrots so you can dig them as you need them through the winter. Just pick the kale when you need some.
The tops & leaves of dead garden plants should normally go in the compost pile - use tree leaves for leaf mulch. This is a step in the direction of disease/pest mitigation.
After that, many options depending on how you want to go. You could plant a cover crop (winter rye) to be turned under in the spring. You could mulch with shredded leaves, or buy straw, or pile on 3-6" of manure, or combine all three, or do different things to different beds to see what you prefer.