Why should I compost?
Composting enriches your garden, while reducing waste that would otherwise go into the landfill. In a landfill environment, plant waste, such as food scraps, creates dangerous methane gas. You can recycle your plant waste into compost that replenishes your garden soil with organic matter for free, keeping it all onsite--sustainability at its best!
Do I need special equipment to compost?
As long as you have outdoor space, you do not need any equipment. The earth has been composting long before we thought to do it; you just need to create the right conditions.
What can I compost?
To keep compost processes simple, as well as safe, keep it to plant waste. This means food scraps, grass clippings, leaves, and plant-based products like paper or cardboard. Two exceptions are: egg shells and manure.
Note: Compostable products like plastic-like forks, straws, and plates are usually compostable only in industrial, high-heat settings and won't break down in a typical backyard compost pile.
How do I compost?
Size and Location
A 3′ by 3′ area or larger is needed to create an effective compost pile and you should aim to pile material 3′ high also. Locate your pile in an area that isn't soggy, doesn't pool with water, and is in part shade, if possible.
Style/structure
A structure is not needed to start recycling your plant waste, just a pile with the right ratio of ingredients. However, you can build a structure to enclose the compost to make it look tidy or even have multiple bins to separate compost in different stages of completion. A structure that is enclosed or uses ¼″ hardware cloth (wire mesh with ¼" openings) is useful for keeping hungry wildlife or even the neighbor's dog at bay.
Compost Ingredients
Let's talk ingredients. You may have heard the terms "green" or "brown" material--let's dive into what they are.
Green materials are fresh plant materials like green grass clippings, fresh leaves, fresh landscaping trimmings (except wood), vegetable kitchen scraps, and plant-based animal manures. Green materials are high in nitrogen, a nutrient that tends to move into the atmosphere as plants dry or are processed, turning them into brown materials that are more carbon-rich. 
Brown materials include dried grass clippings, dried leaves, dried landscaping trimmings, fresh or dried wood, and also processed plant material like paper or cardboard. Wood ash can be added but it increases pH so avoid it if you have naturally alkaline soil.
The ratio of nitrogen to carbon in a pile is ideally 1:30 to keep microbes working hard to break down material and to heat the pile. This isn't a volume or weight of green to brown material, rather, a ratio of the actual nutrients in the materials you add, which varies among different materials. This ratio is a good start to understand how much green and brown material should go in a pile, but some simple observations of your compost's smell or progress (see Troubleshooting below) will help you know if you are on track or how to correct if not.
You can also add composting worms, called "red wiggler worms" to an open pile or an enclosed pile that is in contact with the soil. These worms are ideal helpers in your compost pile. They are cold-sensitive so they may retreat into the soil in the winter and reappear in the spring when temperatures warm.
Maintaining Your Compost
In order for your well-balanced compost pile to turn into a nice, rich, finished product, it needs time, warmth, air, and moisture.
Turn your pile (mix by moving the inside to the outside and so on] to add air, which speeds the decomposition process. Allow at least 2 weeks between turns to allow the pile to heat up again.
An ideal compost pile will have the moisture of a rung-out sponge. How often you need to add water depends on your climate, so just give it a feel from time to time. Mulching your pile with a layer of brown material will help retain moisture, but that material should be removed before turning. A tarp can also be used to retain moisture.
When is my compost ready?
To a degree, the more you turn your pile, the faster it will decompose, but in general, expect your compost to take 3 months to a year or longer to be "finished", depending on ingredients, size of ingredients (smaller particles are faster), frequency of turning, and other conditions like moisture, air, and temperature (e.g., summer composting is faster than winter).
Look for your compost to be a rich, dark brown, and for particles to be broken down. Items like egg shells and sticks may still be large and need to be broken up, added to a new pile, or screened out with a mesh screen (hardware cloth attached to a wood frame).
How do I use my compost?
Simply mulch your beds with ½″ to 2″ layer of compost or work it into the soil.
Compost troubleshooting
The speed of decomposition and odor of your compost are excellent indicators of how healthy your compost pile is. You compost should smell "earthy" and after a few turns you should be seeing some progress (i.e. decomposition).
Compost isn't heating up or progressing
Your pile could be too small or needs more nitrogen or moisture. This can also happen in the winter months due to cool temperatures. Adding manure to the pile for the winter months can help heat things up.
Foul odor
A sulfur odor is an indicator of too much water or not enough air. Aerate your pile by turning it and add more brown ingredients if it appears to be too wet.
An ammonia odor indicates the pile has too much nitrogen/green material; add carbon/brown material.
That's it!
Congratulations on taking a big step to reducing waste and replenishing your garden! As with most things, composting can be a little intimidating at first, but once you give it a try, you will realize that maintaining a good compost pile is pretty simple and very rewarding.