I wont lie - I am totally rubbish at knowing my left from my right so I have never actually taught my dogs 'left' and 'right' on an agility course
But I have found this a useful trick for many reasons. Firstly it teaches you and your dog about luring and phasing out the lure (I teach this trick to a new dog just after I have started teaching them 'sit') It is good for warming up muscles and getting focus. It can be great fun for the dog so great for cheering them up when they are a bit down or unmotivated and it gets dogs comfy with turning away from you and you crossing behind them as a starter to flicks and rear crosses
I usually start with the dog infront of me and a treat in my right hand. I lure the dogs nose clockwise and reward for the nose moving, then reward for 1 step to the right, 2 steps, 4 steps and then a little jackpot for them getting all the way around. (sometimes bigger/less flexable dogs need a bit more space so I lure and take a step back.
Once they have done a couple of full circles with a lure in my hand I then remove the treat from my hand and lure with an empty hand and reward from my other hand
Slowly over time move the lure hand higher and higher and make your circles smaller until you are just pointing in the direction you want them to go.
Add the cue word ('right') when you know they will take the full circle and say it as they are circling, I dont try saying the word before the action until they can do it with just the finger point then I would say 'right' wait a sec then point - if the dog does it before the hand signal then they get a jackpot
Remember and work on the other side (left) as well