Overview:
Compost is organic material that can be used as a soil amendment or as a medium to grow plants. Mature compost is a stable material with a content called humus that is dark brown or black and has a soil-like, earthy smell. It is created by: combining organic wastes (e.g., yard trimmings, food wastes, manures) in proper ratios into piles, rows, or vessels; adding bulking agents (e.g., wood chips) as necessary to accelerate the breakdown of organic materials; and allowing the finished material to fully stabilize and mature through a curing process.
Source: Composting Basics | Wastes | US EPA

 

In MotherEarthNews tests, tumblers did not produce finished compost any faster than a well-managed compost bin or open pile.

Master Composter Barbara Conover says that unless you have a very large pile a bin works better.

Batch (In-vessel) Compositors:
In batch composting, kitchen scraps and dry leaves are added to a bin until it's full, and then nothing more is added so that it can all finish breaking down, which may take 2-3 months. With big accessible batch bins, the compost should be turned a couple of times over the course of 2-3 months, to give it air, re-mix the contents, and keep it from smelling. This is the best way to generate a lot of compost for big gardens, or if you eat a LOT of vegetables and want to compost all the scraps.

In batch composting, you really need at least 2 bins so that one can be active (where you add new stuff) and one can be closed (where nothing new is added so it can finish decomposing). The one to the right has 'active' and 'finishing' bins and is good for small quantities.
You should get 2 of the single batch versions shown to the left.

Center-axle drums. A vertically mounted drum rotates around a central, horizontal axle supported by a wood, metal or PVC frame. Operation is generally easy, particularly with the models that have doors on both ends. The central axle acts to break up and mix the materials. Most of these tumblers are mounted low to the ground, however, so emptying them can be a chore unless you have a low-boy wheelbarrow that happens to fit under them.

Base rolling drums. A horizontally configured drum rolls on a ground-level base. Some of them actually have rollers, while others have molded rounded points to suspend the drum and let it rotate. Obviously, the tumblers with rollers are easier to turn. To help make rotating easier, several of this style have steps molded into the body, so you can use your feet and legs to turn them, thus theoretically easing back strain.

Top-to-Bottom Composters
In a top-to-bottom composter, kitchen scraps and yard waste are continually added to the top of the bin, and finished compost is scooped out of a little door at the bottom. The new stuff is always on top, pushing the older and more decomposed stuff toward the bottom. Most molded plastic compost bins work this way. This is a slower process because the contents in the middle of the bin are hard to access for turning and aeration and therefore are slower to break down. These types of compost bins won't make a lot of compost quickly, but on the other hand they require almost no effort! They will make enough compost to supply most patio, container, or other small gardens.

Composting with Worms:
Worm composting is using worms to recycle food scraps and other organic material into a valuable soil amendment called vermicompost, or worm compost.

We recommend using only raw fruit and vegetable scraps. Stay away from meats, oils and dairy products, which are more complex materials than fruits and vegetables. Thus, they take longer to break down and can attract pests. Cooked foods are often oily or buttery, which can also attract pests.

Avoid orange rinds and other citrus fruits, which are too acidic, and can attract fruit flies. Try to use a variety of materials. We have found the more vegetable matter, the better the worm bin. Stay away from onions and broccoli which tend to have a strong odor.

You should use red worms or red wigglers in the worm bin, which can be ordered from a worm farm and mailed to your school.

Liquid that comes off the bottom can be used, but check the difference between Leachate (the raw runoff) and worm tea (brewed with worm castings) at Leachate vs. Worm Compost Tea | Nature's Footprint. See:
Worm Composting Basics - Cornell Composting

Products:
Compost plastic composters - TheFind
WalMart
Rain Barrels & Compost | Wayfair
Gardening & Lawn Care : Composting Bins | Hayneedle.com
Amazon.com: Composting Bins

Compost Wizard $112 [4.0, 246]	Yimby $104 [4.4, 195]	Juwel 77 gal $105 [4.4, 7] AEROPLUS 6000 140 gal $250 AEROQUICK 290 77 gal.	Green Culture 65 gal $53 [4.1, 26]
Worm Factory $110 [4.6, 297]	Urban Compost Tumbler $329 Amazon $379 [2.8, 12]	Algreen Soil Saver Classic 88 gal $83 [4.1, 178]