The biggest help a compost pile can receive is to cut or chop up materials into smaller pieces.  When pulling out spent plants, throwing the entire plant into the compost bin will inevitable yield finished compost.  However, by cutting the plants up into the smaller pieces, there is a lot less work to be done by the microbes in the pile to break down the material.  Smaller pieces equals a fraction of the time to finished compost.  There is also more surface area on smaller pieces for microbes to do their work.

For bigger jobs, such as branches from trees and shrubs, a chipper makes quick work of taking a difficult to compost item into ideal compost material - and it keeps the branches out of the landfill.  (Make sure to read all the safety instructions before operating a chipper.)  Then throw the wood chips into the compost, spray with a bit of water to moisten the pile and give it a quick stir with a garden fork.

Bonus: Another use for the chipped branches as mulch, just leave them in a pile to age for a month and then spread them around your plants.