Alocasia is more commonly known as Elephant Ears, due to the very large heart shaped leaves on the plant. There are many varieties of the plant and some that will grow over 15 feet tall. You can purchase these plants at nurseries or start your own from bulbs. Some species are very tropical and don't like the cold but most are pretty cold hardy and will come back after a winter frost. None are recommended for gardening zones north of zone 7. These plants like water and humidity but are relatively easy to care for.
Choose a location that has full sun for large growth or partial shade if you want to keep the plant smaller. Most species like to be very wet, so if you have an area that stays moist to wet, this is a good place to plant. They may get very large so be careful not to shade other plants that need sun.
Dig an area a few inches larger than the pot you purchased the plant in. Mix a few handfuls of compost in with the dug-out soil. These plants don't require excellent drainage, but do like rich, nutritious soil.
Add some of the amended soil back into the hole and place the plant in at the same level as is in the container you purchased it in. Fill in around the root and water well to compact the soil. Continue to fill so the soil is level with surrounding ground.
Water until the soil is wet. Continue to water every day until the roots are established in their new environment. Then you can cut back to every other day for a couple of weeks. After that, water as soon as the soil starts to dry out.
Fertilize with a 20-20-20 fertilizer at half strength every 3 weeks from the time you start to see growth until late fall.
Mulch around the plant to hold in the moisture. Using a pine needle or grass cuttings mulch will also provide the plant with some extra nitrogen that helps grow nice green, thick foliage.
Cut off brown or yellowing leaves at the end of the season. Leave all green leaves attached as they will make the food for the next growing season. In some warmer areas, they plants may only go dormant for a few weeks.