A shredder\chipper would be great, wish I had one. I know various places rent out that kind of equipment (along with commercial restaurant\hospitality stuff). You could in theory rent a chipper (around here we call them mulchers) on certain occasions, like at the end of fall when you have an abundance of leaves. You could mulch them and store enough for later use.
At the very least you can work with a lawnmower, food-processor and\or coffee grinder. Otherwise you have to cut up everything, by hand, or you'll be waiting more like half a year for finished compost. There can be some sticks\twigs and chunkier pieces, but the smaller the particles are the faster the bacteria can get to work decomposing them. In nature when a tree sheds its leaves, the leaves fall and gather (on the floor of a forest, for example). In this case various exogenous forces begin to decay the leaves: the lower level of the litter will retain enough moisture that saprophytic fungi can begin to colonize the material. The fungi can digest the more complex carbohydrates (cellulose) within the leaves and they can physically penetrate solid materials with their hyphae and digest it enzymatically. Fungi can also digest lignin, which isn't a carbohydrate but is found in woody materials (and in leaf twigs), encompassing the cellulose and giving the wood it's strength.
Bacteria, on the other hand, are single celled organisms. They typically need more moisture to live and can only work on the surface of a material. Only special kinds of bacteria can break down cellulose and even less are capable of breaking down lignin or other more complex compounds. But, they are still primary decomposers, adept at going for soft and easy to digest materials and able to proliferate rapidly. They move in once the fungi have taken care of the cellulose and the material is broken down sufficiently. Aerobic bacteria produce heat as a result of their metabolism, and they are the organisms primarily responsible for heating up a man-made compost pile.
So if we want rapid thermophilic compost we must break down the materials first ourselves; otherwise we have to wait for fungi, arthropods and other animals to exert actions that open the materials up for bacteria naturally. You'll also need enough of the right materials for a pile large enough to heat up, it should be at least 3' x 3'. The microbes need carbon to fuel their metabolism, and nitrogen to build amino acids\proteins in order to live. Fresh green materials also contain the simple sugars bacteria like. Materials should also be mixed at the correct ratio of C:N which is roughly 30:1. This will ensure properly paced decay, resulting in sweet smelling compost without burning away the nutrients.
The fresher the greens the more nitrogen will be present in the material. Fresh grass clippings are probably the best green material (19:1) and should be abundant obviously if you have a lawn. Try to ensure the blade on the mower is sufficiently sharp so it gets mulched good and bag some of the clippings. When you empty the bag lay the clippings out in the sun so they'll dry out before adding them to the compost. If you add wet clippings you have to do it layered in with drier brown material, otherwise the clippings will clump up and provide pockets of anaerobic conditions. Alfalfa is another good green material as snew recommended and you can find it at animal feed stores.
Fallen autumn leaves are a popular brown material. Sphagnum peat moss is also a brown material with about the same ratio of carbon (50:1). Many regular home improvement stores sell sphagnum in large bales in the garden center. Coffee grounds, tea bags, parper towels, newspapers and cardboard are also brown materials, along with other woody materials.
Grass clippings and/or alfalfa with dry leaves and/or sphagnum can be mixed together to provide a quick basis for a compost pile. You can throw down some sticks, twigs, tree bark, etc. in order to give it a foundation and allow for some air exchange underneath. It helps to get a compost starter\activator that has microbes. Espoma and other companies sell them. Otherwise you could just use a dry organic fertilizer like Espoma Garden, Plant or Holly-Tone (also sold at Lowes\Home Depot) and sprinkle several cups in with your materials. Mix it up and moisten it, plain water will do but if you can use some molasses or better yet a compost tea to stimulate\impart microbes onto the pile. If you've done it correctly it should really heat up within a couple of days. Turn your pile daily and if it isn't too hot continue to add in your kitchen\yard scraps.