Making compost is very easy as nature does most of the work for you!

There are billions of micro-organisms in soil which break down dead plant material. To make sure you have plenty of them in your bin put your bin on soil.
You can add extra soil to your bin: this can be attached to weed roots or you can sprinkle an occasional handful of topsoil into the bin. Your bin will be quite smelly without this soil.

Site your bin in a sunny spot. The material you put in will break down more quickly when the bin is hot and high temperatures will kill off many weed seeds. The micro-organisms like it hot. It will take much longer to make compost if your bin is in a shady place and you will get weedy compost.

Keep the heap moist, but not soggy. The compost can sometimes dry out at the edges, especially if there are slatted sides, so watch out for this in dry weather and water the contents of your bin if necessary. Those precious micro-organisms may die if they dry up.

Micro-organisms need air, so don’t pack down the compostibles. Fresh compost at the top of the bin can be roughly mixed with a fork to inject fresh air into the middle of the pile.

You get best results from A good mix of green, sappy materials, (grass clippings, vegetable peelings and weeds ) with brown, fibrous material (stalky stems, cardboard, crumpled paper).

The larger the bits you put in the larger the lumps you will take out: try to break up or shred bigger stems and compostibles. The micro-organisms will take a long time to break down large lumps.

What to put in the bin  
Vegetable and fruit peelings   Dead flowers   Stalks of plants you have cut back   Annual weeds   Tea leaves
Coffee grounds and Egg shells   Grass clippings, if free of synthetic chemicals   Soft Evergreen clippings
Straw, hay and leaves   Vacuum dust   Animal manure [not dog or cat]   Crumpled paper   Cardboard egg boxes   small amounts of wood ash

What to avoid in a general purpose bin
Wood shavings and sawdust (these rot down but they may take several years to do so)  
Branches and prickly prunings (for how to deal with these see Woody Prunings and Prickly prunings)  
More grass than makes a 30cm (1foot) layer (for advice on dealing with lots of grass see Grass and Leaves and Too much grass
Perennial weed roots, the leaves are safe to put in (for how to deal with perennial weeds see Perennial Weeds and Weeds

What not to put in any bin
Cooked food and bones (may attract rats), unless you are using a Green Cone  
Disposable nappies   cellophane wrappers   juice cartons   ash from a coal fire