You need to add carbon materials to your compost pile to provide energy for microorganisms while they break down your organic matter. Carbons for the compost pile include the following:
Dry leaves: Dry leaves are probably the easiest brown ingredient to work with for a beginning composter because they're already smallish pieces of organic matter that are easy to shred into even tinier pieces if you choose. They're also in abundant supply in most regions and turn into fairly decent finished compost (called leaf mold) all by themselves.
Woody plant trimmings: Shrubs, trees, palm fronds, dead perennial stems, Brussels sprout stalks, and dried cornstalks all fit into this category. Break, chop, and shred this material as much as possible to speed decomposition.
Paper: Shredded paper is great for worm bin bedding. Other paper products that are easy to shred or tear include used paper towels, envelopes, paperboard (unwaxed cereal and food boxes), paper towel and toilet tissue rolls, and newspaper.
Cardboard is slow to compost, and the thicker corrugated stuff is hard to tear, although it works well for soaking up excess moisture in wet ingredients. Tear it and mix it with fresh manure or grass clippings, or lay it on the bottom of a pile if you're composting in a damp region.
Straw: Made from the remaining dried stalks of cereal grains (wheat, oats, rye, barley) after the grain has been threshed and removed, straw is used primarily for livestock bedding. It's used less frequently than hay as livestock feed because straw's nutritional value and digestibility are low. You can use straw in the garden as mulch; it's safer to use than hay because it contains few weed seeds.
Pine needles: The resinous coating on needles can take a while to break down, so use them in limited quantity. If you have a lot of pine needles, you can easily stockpile them and gradually mix them in with other organic materials. (Pine needles also make attractive and effective mulch spread around garden beds.) Don't worry about pine needles' acidity unless you have a lot of them: Small amounts have minimal effect in your compost pile or soil.
Sawdust: Because sawdust has an extremely high carbon to nitrogen ratio, use it sparingly in the compost pile. Sandwich an ultra-thin layer (no more than an inch) between moist grass clippings, or mix handfuls thoroughly with lots of other ingredients.
Thick layers of sawdust compress into impenetrable mats, reducing the ability of oxygen and water to circulate through the pile. Also, decomposers start to work on sawdust as they do every other ingredient, but because of the high carbon load, they require copious amounts of nitrogen-rich material over time to process all that carbon. Sprinkling small amounts of sawdust you generate in your woodshop won't hurt the process; dumping huge amounts from the local sawmill will shut it down.