A ponytail palm tree is neither a palm nor a tree. In fact, it is a member of the Agave family and is actually a succulent. It stores water in its elephant foot like trunk which is another common name for it.
Since this plant is a succulent, it grows best in semi-dry conditions. Let the soil dry out significantly in between waterings.
Ponytail palm needs bright light, but it is a forgiving plant. As long as you place it outdoors in the summer, it will tolerate any indoor light conditions you keep it in during the winter.
Let them get root bound before repotting.