Let's go back to foundation training. When introducing any new obstacle, you want to keep the difficulty low and emphasize the fun and ease that it can be for your dog. If your dog has a sit stay, leave him about 2 feet in front of the tire, facing it, walk to the other side and call your dog, "Come Tire". If he won't budge, put your hand with his treat or toy through the tire to coax him to follow your hand and jump through the tire. Practice this several times until he willing is coming to you. Keep him about 2 feet from the tire, you go to the other side and then move back about 6 feet, "Come Tire. When your dog is able to jump through the tire when you are at different distances and angles from the tire, then it is time to move him further away from the tire. Start him back 6 feet, you go to the other side about 6 feet away and call, "Come Tire". Place your dog at different distances and angles from the tire and call him to you. When your dog can succeed 80% of the time, its time to progress to make the challenge a bit harder.
Now that your dog is coming to you, it is time to teach "Go Tire". Start close to the tire again, 3 feet away, this time both you and your dog are facing the tire. Tell him "Go Tire". If he jumps through, great, step to the side and reward him. If you don't get any movement from the dog, step forward and point to the tire, "Go Jump". For some dogs this motion on your part is enough to get them up and going through the tire. If your dog still won't move, take your treat container or toy and throw through the tire, saying, "Go Tire". Repeat this many times until your dog will successfully go through the tire without you having to step toward the tire or throw his toy through the tire. If you are using a toy quickly try to get your dog to go through the tire then reward with a throw of the toy or treat container. Begin to back away from the tire, 3 feet, 6 feet, 9 feet work toward sending your dog from 30 feet away.
If you've started with a very young dog you should still have the tire height set low 8" or 12" for a good bit of your training. If your dog is older and large, now begin to move the tire height up. Go back and practice you "Come Tire" and "Go Tire" when you change the heights. As you raise the height your dog may try to go under the tire. At first you may want to setup some wire mesh or angled jump bars under the tire for your dog to realize he still needs to go through and not under the tire. When you are getting ready for competition, raise the tire slightly higher than your dog would have in the agility ring. Preparation and practice are the best training tips for succeeding in the competition ring.
