Sadly, composting is not something that just happens... Well, obviously it does just happen but for it to happen efficiently takes a bit of work. To be brutally honest not many of us have the space for a compost heap or the inclination to nurture it but something has to be done with the garden waste we produce and consigning it to a land fill site is not the answer.
If you maintain your own garden you need to do something with your garden waste. Most local authorities have collection points where you can deposit green waste, they will also arrange for a regular collection at a price. Be very wary of paying people to dispose of your garden waste at knock down prices. It is illegal to introduce some plant species into the wild and if you pay someone and they ultimately fly tip the waste in a field or road side you may be held accountable in law.
The biggest mistake which people make when home composting is piling up huge mounds of grass clippings and waiting for something to happen. Grass clippings are mainly nitrogen rich and an effective compost heap needs a high level of carbon, hence you need to add woody waste, paper and even cardboard. Ideally all waste should be shredded to accelerate the composting action and the heap needs to be turned frequently to get oxygen into the mixture. If you have a compost bin you need to turn the mixture regularly so, although they are more expensive "tumbling" composters are a better option. Ideally your compost should heat up so that it steams on a winter morning
Vermiculture is fun and an efficient way of dealing with small amounts of kitchen waste. Although wormeries can be expensive to buy they can be made at home quite easily and inexpensively. A small wormery can be kept in a corner of the garage or simply tucked into a corner of the garden where it will produce a rich black compost and a liquid plant feed without odour or hard labour.
Never add cooked food to compost as it attracts vermin. Likewise never add cat, dog or human faeces. Apart from the smell any pathogens are unlikely to be destroyed.