To make compost successfully, you will need some form of bin. You need to contain your compost to stop a heap spreading in an uncontrolled manner across the garden.

Four stakes and some wire netting in its simplest form would do. Old pallets would also do the job.
Where space is limited and looks are important there are purpose-made units of various designs. Much successful composting depends on keeping the temperature up. Some top-of-the-range systems involve insulated panels to achieve this.

The sort of stuff to aim to put in would be soft plant material. Avoid scraps from the kitchen such as meats or cooked food for fear of attracting vermin.
Use uncooked waste vegetable material by all means, but anything organic would be suitable. Newspaper and even wool will rot down. Many will want to use grass cuttings, but these need mixing with other material. Avoid weeds that have seeds attached or diseased material.
Woody material should also be shunned as it is slow to rot. But much more use of this could be made if it goes through a shredder first, pulverising it and mashing it into something more fibrous. These machines are great if you are keen or have a large garden.

At the heart of it all is the microbes that do the work. Friendly bacteria will work away at turning everything you put onto the heap into something that you can return to the soil.
However, we can greatly speed the rotting process by encouraging our tiny helpers. We have already said that they like to be kept warm – a cover will stop heat escaping, although this will be tempered with the need to allow some moisture into the heap.

Never use fresh tap water for this as it contains chlorine designed to keep us free of harmful bacteria, but will reduce numbers in the heap.
Chlorine is volatile stuff and will dissipate after 24 hours or so if left in a bucket or the like before use. Better still use rainwater you have collected.

Bacteria need oxygen to breathe so it is important to turn the heap every now and again.
You can buy a compost tumbler – something which looks like a water butt – which can be rotated on a stand. Or you could use two heaps turning compost from one side to another.

If not, the compost bacteria run out of air and the process slows to a halt.
This often happens if only grass cuttings are on the heap. Much heat is produced at first but the process comes to a stop if the heap is not turned.

In a totally airless environment the compost turns to a black gooey mess. You will have seen this if you have left grass in a plastic sack. It does not make good compost!
There is one other thing that can happen. As the rotting process moves along it can become more acidic which slows it down. You could add a little lime to help this or indeed one of the proprietary compost accelerators. These contain nitrogen as well as some lime. The former is in there to feed the bacteria and will help them to work faster.
What should come from this process is a product unrecognisable from the original constituents being dark brown and crumbly.

It is a satisfying thing to achieve and like much in the garden is perfectly attainable if you put the effort in.