Keep the compost moist and oxygenated.
This means rotating the drum regularly to add oxygen, and adding water when the compost gets dry.

Keep the compost warm.
This is not usually a concern because the compost in the drum and the drum’s insulating properties keep the heat in.

Aim for the right carbon/nitrogen ratio.
Adding a mixture of kitchen and regular yard waste is effective, but for better, faster results, add carbon-rich material (browns) like sawdust, straw, dry leaves, or wood chips. These balance the nitrogen-rich green material and kitchen waste. Chop up the waste if possible: the smaller it is, the faster the breakdown process.

If you use only kitchen waste, you may need to add bulking material or pre-composted material to help with oxygen penetration as the drum rotates.