Set up the tank, wash the sand first, then fill almost full of water. Put the Safe Start in, then transfer the betta to a bag or the cup he came in, and let it float in the tank. If you use the cup make sure it doesn't topple over. After 15 minutes, the water in the cup or bag will be the same as the tank so just tip the cup/bag over and let him swim out in his own time. Since you moved him to the 1 gallon, I assume you used tap water? If so, you don't need to acclimate him using the drip method like you would if he was in store water.
The reason I said to fill the tank almost full is so there's room for the water in the bag/cup. If it's not full afterward, you can top up the tank then.