I'm sure there are as many methods of this as there are gardeners. I've gone through various stages myself. I used to pull everything out, compost it, and leave the soil bare with the plan of tilling in the spring. When I made this garden I decided on raised beds and no more tilling; I felt it was damaging to the soil. For several years I would leave some things in the garden as shelter and food for animals (and I still leave some sunflowers) and then just start a new compost pile with those things in the spring. A few years ago I discovered that the mulch that I was using to keep weeds down and soil moist all summer also protected my soil all winter and made it harder for weeds to sprout in the spring. I'm all about not having to deal with excess weeds so I decided to become more of a year-round mulcher.
Now I collect grass clippings and bags of leaves from my neighbours (all year) and use them to mulch every bit of each garden bed. (those garbage bags you can see in the photo are full of neighbours' leaves) The soil stays protected, the worms are happier (you know I like a happy worm), the soil is improved as this protective layer breaks down and, come spring, there are no weeds popping up on my beds. Mulching makes gardening easier for me. It's that simple.
So...to answer your questions, Jess - I do put all my plant waste in the compost at the end of the growing season (except for the very thick main stems of my tomato plants and sunflower stalks. Oh what I would do for a shredder). I don't dig up or break up my soil anymore because it is in beds and stays quite loose. I just keep piling on more mulch to add more organic matter and the worms loosen up the soil for me (I haven't used a tiller for at least 8 years). When it is planting time I will just nudge some of the mulch (that hasn't broken down) aside and plant my plants. It's a win-win-win situation. For some things - like lettuce or carrots- I do still clear away the mulch so that the seeds can sprout more easily but most things do well with the mulch all around.
Hope that helps. Have fun. One of the things that I love about gardening is that the garden tends to be a very forgiving teacher - there really is no right or wrong in the garden. You know?
Now I want to get out there and use up those last bags of leaves. ;-)