Basically, all you need to do is to keep the Composter fueled and filled up with organic matter. After a while it will make COCompost for you which you can sell at a profit to the bazaar.
What’s the best composter fuel?
Just use whatever fuel is recommended below.
Does this work while offline?
Yes, the composter fully works while offline, while on a different island, etc.. You should consider upgrading the Organic Matter Cap and later the Fuel Cap so you can get more compost overnight.
What makes a good organic matter source?
Usually, you want to find something that has a high amount of organic matter for a good price. So, for example, you may want to buy ESEnchanted Seeds over SESeeds as that means you will need to buy a lot less items overall.