It does really depend on what type of palm it is. But for most palms, it is important not to overwater. Water when the soil is almost dry to the touch. Frequent misting with a spray bottle of water is beneficial, especially when new leaves are about to open. Fertilize every two weeks with a water soluble fertilizer.
I cut off stems that are yellow immediately. They won't green up again, and are serving no purpose to the
plant once they turn solid yellow.
If you could post what type of palm you have, I might be able to help you with more specific info.
