The best time to plant basil in Las Vegas is in January or February, from seed. You should start the seed indoors and move the plants outdoors after the last frost date. In Las Vegas, this is around March 10. If you are using starter plants, do not put them outdoors until after March 10.
Use a rich soil that includes a lot of compost. This type of soil holds moisture better than a lighter soil.
Keep the soil moist at all times and offer protection from the afternoon sun. A wood mulch over the soil helps to preserve moisture and, if grown in pots, you can move the pots to a shady location during the heat of the Las Vegas afternoon.