1. Observe your tree and be gentle
This new tree is rapidly growing in ways that we can't even see and we have to be careful not to damage tender new growth and roots. Harsh chemicals can burn new, sensitive roots like harsh soaps can damage a baby's skin. It is important to correct any problems speedily and in the appropriate manner. I don't recommend anything other than organic sprays or treatments when the plant is new, with the exception of slow release fertilizers since they don't dump a large amount of chemicals at one time. I know even knew trees can get caterpillars or insects, but you may need to let it go for the season or treat with a safe and gentle organic option.
2. How to water over time?
Now, I recommended a deep watering with a hose for newly planted trees. Be careful not to damage the trunk with water spray. Set the hose to a trickle and let the area inside the berm of mulch fill with water.
If you are planting in the heat of summer, and it is HOT summer so far, you should continue with that kind of deep watering for about a month. For the first week or two, I recommend water every day. Then you can switch down to every other day for two weeks, and then down to 1-2 times per week until the heat breaks in September.
If you are planting in a cooler season, I would recommend cutting the water schedule in half. Only one week at every day, one week at every other, a third week at every third day, and then down to once per week unless it rains.
The most important thing about watering is to watch your tree. In the heat you want to watch out for leaf curl and wilting as signs that the tree isn't getting enough water. Any yellowing or lime green on the leaves is usually a sign of overwatering and can be treated by cutting back on the water and applying iron to green-up the tree.
3. Stakes and mulch as you move forward
When the tree was planted, you made a berm of mulch about 4" tall at the edge of the planting hole. This serves to keep water in as well as reduce weed competition. I would leave that berm for the first year. If you need to add mulch you can, but I would let it decay and collapse on its own. You do have to be careful about filling it in. Don't do that! You do not want to start building up mulch on the trunk. That can lead to disease and problems.
