First mowing of the season: this first cut of the season should be on the short side. The shorter mowing will encourage the roots and grass to wake up and start growing.
Water: only as needed. Again, this depends on your location and climate. If you need to water: water deeply and only once week or so (if there's no rain). Infrequent, but deep waterings will promote deeper roots and stronger/healthier grass (as opposed to frequent/shallow watering). Some people measure the water (putting out cans to see how much water the sprinkler is putting out) and aim for 1 inch per week. The best time to water is early in the day (avoids heat/evaporation).