The easiest way to start a compost pile is to use existing compost (bit chicken and egg). However combining the following materials in a layered system will start by itself, taking slightly longer to start.
The bottom layer of a compost pile needs aeration so piling in bits of wood and sticks ensures a bit of air movement through the bottom. Most composting boxes have ventilation panels around the bottom. Getting a good airflow into the bottom of a compost pile is important.
Thereafter, layers of organic and woody material are added getting the best mix of ingredients available. Organic material from the kitchen (not cooked material or meat) acts as a good activator to get the compost pile working.
Cardboard is a very useful compost material in the city. It requires to be plain cardboard not plastic coated or with plastic tape. It is an ideal dry material to insert between layers of wet material and breaks down easily over the year. A soil layer helps seal up the pile to encourage it start working.
Finally, the yard clean up takes place. It is important in a city garden to ensure the composting area is kept clean and tidy. This is not so much for the compost but for the neighbours. People worry that composting is a dirty business so it is important to demonstrate it is clean and tidy.