Edward,
Positive reinforcement methods like clicker training work wonderfully with basenjis. All four of my basenjis are clicker trained. I guess you could even consider Sophie to have started before birth since I was clicker training her mom while she was pregnant with the litter. The purpose of the clicker is to mark the behavior that you want so you could also just use a word like "yes" or "Yay" or "good dog" followed by a treat.
I use clicker training to train a variety of behaviors such as sit, down, attention, name response, stay, stand, go to mat, front, point, hand targeting, and the list goes on. I also use it in agility training.