The Maya and Aztec mainly grew their food  in small market gardens. The Maya used flooded land by rivers, while the Aztec used  land reclaimed from the lake surrounding the island city where they lived.
The Aztec called their raised gardens chinampa. To make a chinampa, the farmers  made a ring of stakes in the lake, then dredged up mud to fill it. They used mats of reeds to help keep the mud from being washed away.
 They could grow several crops a years in the chinampas.