Compost isn't something that just makes itself. It's worth looking up on Google but I use about 1/3rd green material to 2/3rds brown material (differences will be explained in Googled items. Then a proprietry brand of compost maker such as Garotta added to the mix + some water and turn the mix regularly to get air into it to assist in the breakdown of the material.
Plastic or Wood?
Personally I use 2 plastic containers because I just do not have the room to make a wooden enclosure. One is a semi-cone shaped bin that was supplied by the local council many years ago (I hesitate to say free because it all comes out of the 'rates' as they used to be called so we pay for them eventually anyway!). The other is a 200 litre Compost Tumbler I bought via the internet from a company that recycles food industry used barrels. Both do an excellent job (IF) you remember to tumble and/or turn the material regularly. Just letting it sit in a barrel static for a year will just produce a soggy mess!