Why small Saguaro cactus purchased in August is turning brown on one side?

If it is brown and squishy, then your cactus is rotting (overwatering is usually the problem). If the skin is dry looking, maybe with cracks in it, then your young saguaro is sunburned! Even though it is a desert plant, an immature cactus doesn't have the root system or water reserve to take severe, direct sunlight. That's why in the wild, young cacti are found growing in the partial shade of desert shrubs like creosote. Greenhouse grown cacti have been sheltered and often come with a tag advising you to expose them to direct sunlight gradually. You can drape a light cloth over them to provide some artificial shade. Sunburned cacti can still survive, but the scar will always show.