Watering a Japanese maple is not rocket science, but keeping adequate moisture is crucial. In the tree world Japanese maples are considered shallow rooters. Most feeder roots are within twelve to eighteen inches of the surface for well established older trees. Newly planted trees can have all their roots much shallower that that.
Japanese maples like even soil moisture. On most varieties their leaves are very thin and will dry out and burn quickly when soil moisture is not adequate.
Tip 1 If the tree is planted in the spring, newly planted trees should be monitored daily. Check soil moisture a few inches below the surface. (How?) Water every 2-3 days for the first month. After that, a good watering once a week should be sufficient, but monitor it often as windy days can dry out soil quickly. If the tree is fall planted, water once a week when no rain or snow cover is provided.
Tip 2 Always provide a layer of mulch around Japanese maple trees. This will aid in reducing soil moisture loss due to evaporation. Since the roots are so shallow, the sun and wind can damage the shallow roots if not protected.