Enough water for the soil to be moist six inches down and out to at least the drip line is how much water that queen palm trees [Syagrus romanzoffiana] need. It's important to water before 10 a.m. or after 5 p.m., which is the range outside of the high evaporative rates possible in the full sun that the plant enjoys.
A watering schedule for a recently planted tree may be two or three times a week, depending upon the dryness or wetness of the climate. It may be every 10-14 days once the tree is established.
A soil check can be done along with a visual check. Just put a soil probe or sharp object such as a strong writing instrument, screwdriver or ruler into the soil. The plant is being overwatered if the object comes out muddy. It's being underwatered if the object comes out clean as a whistle. It's appropriately moist if the object is freckled or speckled by soil particles.