Light is a limiting factor when growing fishtail palms because most indoor lighting can't equal the bright light these trees need to thrive. In the outdoors, they grow amidst taller trees that help filter out the light and heat, so plant them in a sunny spot that gets morning sun and less direct light later in the day.
Use a cactus soil mix or a general-purpose potting mix with sand or perlite mixed in to create excellent drainage, because these trees like it on the drier side. Add water to fishtail palms whenever the soil feels dry to the touch, which you can test by sticking a finger in the soil about an inch deep. Damp soil means you don't need to water.
Fishtail palms are fussy about humidity and need at least 50% humidity to grow and stay healthy. Indoors, you can add a humidifier near the tree or place a tray of pebbles in water under its pot. Keep plants away from air vents or drafty areas. If your home is kept between 65ºF and 85ºF, your tree will do fine.
During the fishtail's growing season, add fertilizer once a month after watering. At a minimum, give your tree a slow-release fertilizer every few months. Use fertilizer specifically for palm trees for best results.
There's no need to prune fishtail palms. If you spot dead leaves, trim them off the tree. You can also prune if the tree is getting too large for your space. Trim the tops of leaves at the top of the tree to prevent it from growing taller.