This Spring, I pruned all my shrubs and pulled out a few pine stumps. My first thought was just to pile them all up on their own. I have never had good luck trying to compost such material with the rest of my compost. But I'm concerned that these heavy materials will take years to compost all by themselves. What can I do to speed up the decomposition of such materials?
That is very woody material. Wood takes time to compost - probably years for your stuff. You need to do two things: break it into small pieces, and mix it with other material.
The shrubbery cuttings might be choppable by hand - but it could take time. That isn't practical for a tree. You really do need to rent a chipper. And if this is a regular occurrence, then you'll want to eventually buy one (rent one first so you don't over-buy or under-buy).
As for mixing stuff: I would mix with grass clippings (and start collecting them if you currently use a mulching mower) and kitchen waste (vegetable peelings, coffee, etc). You want to get a good mix. For a large heap, most people do this by layering.
An alternative would be hugelkultur. I'd never heard of it until it came up in a question on this site last week. This is a form of slow in-situ composting. Basically you put the wood in the base of your beds and it decomposes over years, slowly releasing nutrients. Never tried it but if renting a chipper really isn't an option, then this is probably the only alternative (other than giving it to your local city's trash/tip services).
I also agree with the Hugelkulture beds mentioned above. You can just place all the branches and logs in a pile or several piles and put everything that you want to compost over top of them and then cover with either soil or invertred sod and mulch.
If you cover with soil you can plant in it right away. I have made several hugel beds in my gardens and they have all done wonderfully. As the wood rots it feeds the soil and holds moisture.
These can be done as raised beds, or dug into the soil
I've been reading permaculture blogs on chippers and what to do with piles of branches as I have the same problem. The permaculture argument is that making the material small with a chipper does cause more rapid decomposition, but in a compost pile there is so much loss of nutrients like carbon and nitrogen, which evaporate during composting, before the material even touches your garden bed. They advocate using wood chipping with discretion, only when you need fine material, only when it is really the only way forward. Otherwise the branches should lie on the soil as mulch, or be buried. Not having a chipper, and having done massive amounts of pruning to curtail the abundance of our urban plot spilling onto the street and inconveniencing the public, I tried to adhere to the permaculturist's recommendations and resorted a stuffing the twigs and branches tightly in under the bushes I had cut them from. There they will shed their leaves and return those nutrients to the soil. When they dry out I will smash them with a garden fork and reduce the volume. Larger branches will be shortened with the chain saw and used for the pizza oven. I cannot afford the time to stand lopping and clipping to reduce the tree branches in volume, sorting them into sticks for mulching, firewood etc. However it is a very effective option if you have the time. The last time I reduced a pile with hand clipping, it took several days to process a few cubic meters. I have a tiny garden and I don't have the space to leave large composting piles everywhere. The garden is 'full' so burying the wood is not an option. Hugelkultur doesn't work here, its so dry that the pile just oxidizes. To reduce branches you either need time (to cut them by hand) or space (to leave them lying around till they rot) or energy for the chipper fuel and your own labour. No way around that, so stuffing the branches out of site, in the dead space under the bushes and trees was the best and most close to nature compromise. You can see the photos on my current post on Home firstname.lastname@example.org on facebook.