Answer: You can add all of it to the compost pile. Initially you will notice that some materials break down faster than others, hence the quicker disappearance of the nitrogen rich "poop" and fresh veggie scraps and then the predominance of longer lasting, more carbon-rich cedar and pine chips. The more active (hotter) your pile, the faster they will break down.
Keep in mind that composting slows dramatically in cold weather and speeds up in warm weather. Wood chips, depending on the size and on the ingredients in your compost, can take a year or longer to compost. You can speed it up by adding more nitrogen rich materials. Green grass clippings, fresh veggie peelings and fresh manure all have high nitrogen content and will help the pile become active and heat up. It also needs to be kept slightly damp as well as aerated to facilitate the active composting process.
To provide the best composting conditions, many folks will run three piles at a time. One is for additions being stockpiled until there is enough material to build a working pile.
The working pile is composed of a mix of ingredients with both nitrogen rich ("hot or green stuff") and carbon rich ingredients ("brown stuff"). Smaller particles will break down faster so some gardeners will use a shredder. Dampen that pile and allow it to compost actively -- when it slows down you then turn it to speed up the process again.
Once it has heated and cooled several times, it will be "finished" and can be used. This finished compost can be sifted with any large particles returned for additional composting if desired. So at any given time you would have three categories -- waiting, in process, and done.
Alternatively you can use a more passive process where you just heap everything up and wait a year or so, then use the resulting broken down material. It still helps to have at least two or three piles though, the oldest one you can take compost from, an aging one that is sitting for its year, and the current one where you currently dump stuff.
I hope this helps.
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