There are three main turns in this game we call Agility, the front cross, the rear cross, and the post turn. When teaching a new dog these fundamental skills it's best to do so without equipment, or on the flat (ground that is). Let's start with the post turn because that's the one that everyone already knows, you just don't realize it yet.
A post turn is a turn 180 deg in the opposite direction. See told you! You do already know it! Everybody learns this neat trick when teaching a dog how to walk nicely on lead. The only change we are going to add is that you practice this with your dog on the left and on the right. I tend to tell my dog "This way!" before turning. It gives the dog a nice little heads up that you're turning and meshes in nicely when out for a nice stroll. I don't use the verbal cue when on the course.
The first of our "walk the line" duo is the front cross. It happens to be the easier of the two. This drill requires that you have food in both hands. One keeps the dog with you, while the other turns the dog. Find a nice long line on the floor to walk along, unless you swear you walk straight, then you can skip it. Start with the dog on the left side, in a loose heel position, and start walking forward - the food in your left hand should keep the dog with you. When you're ready to turn, have your right hand meet your left hand and lure the dog to turn into you, all the while you are turning into the dog. If you've done it correctly your dog should be on your right side focused on the treats in your right hand. The line on the floor is to keep you turning in position, it serves no purpose for the dog. Now repeat to switch the dog to the left side of you. There is so real cue or name for this behavior, but if you feel you need to call it something, call it "switch".
The second of our "walk the line" duo is the rear cross. What makes this one hard is that we have to get the dog to turn away from us as we turn into them. If you happen to notice, the handler turns the same way each times, it's only the dog that changes which way he turns. Set up with food in both hands, dog on the left. Begin walking forward, when you are ready to turn have the right hand meet the left dog and direct his nose away from you and you turn toward the dog. Your dog should now be on your right and you should be setting up to repeat. I tend to call this "flip" because the dog flips out away from you. If your dog does not want to turn, simply break it down into steps. Reward for a head turn, then a neck and one paw, then two, and so on until you have the complete behavior. Make sure to work your dog's hard side more than the easy side, but at the very minimum both side equally.
If at any point you want to make things harder and achieve rock star level, try mixing up which turn you do, then add some speed, and finally some distance. Have fun and happy training!