There is a big difference in heeling for field work and heeling for competitive obedience. In field work, most handlers are happy with heel being a relative position somewhere just off the handlers left side. In competitive obedience, heel is an absolute position where the dog's shoulder is in alignment with the handlers hip and the dog within one body's width of the handler's leg.
Many pro obedience trainers have written volumes on training for the precision that competitive obedience requires. Most begin with a structured attention getting techniques to keep the dogs focus on the handler (rather than in the field as for field work). For most retrievers, the focus of the dog's attention should be on the handlers body somewhere between the waist and shoulders. Drills for attention include treat rewards, either spitting or by hand, while the dog is in heel position and the dog's eyes are focused up at the handler. Again, make sure you know the precise location of the heel position so that you can keep the dog in position.
Initial training after the attention drills, will be simple one pace forward drills, keeping the dog's focus on the handler's shoulders. This position can also be lured by treats in the left hand held above the dog's head and out just in front of where the dogs nose should be. Remember, you need to redefine the heel position from an obscure point just off the handlers left side, to an absolute position where the dogs shoulder is adjacent to the handler's leg. All of this should be done with dog on leash such that the dog can be corrected and placed in the correct position. Also the use of a heeling stick is useful to keep the dog's rear in proper position if the dog crabs or butts out. Also make sure that the treats are given directly over from where the dog's nose should be rather than either by your knee (which will encourage crabing) or off the dogs left shoulder. Also make sure the treats are given using the left hand such that the dog's eyes are up and looking at you.
After you get so the dog can do one step, move out to two steps. Varying your speed and length of step. Again, you are trying to get the dog to recognize that you are asking it to maintain an absolute position with respect to the handler. Keep lengthening your distance but mix it up so the dog anticipate how far you are going; 3 steps fast, one step long, two steps slow, one step short, three steps long, etc.
Next come the turns. Do slight curving turns to the left first. It is easier for you to see your dog and make sure it is in place when you curve to the left. During all of this training, the handler must develop a feel of where the dog is by keeping their eyes focused forward. DO NOT KEEP LOOKING BACK OVER YOUR SHOULDER OR UNDER YOUR ARMPIT AT YOUR DOG AS THIS PUTS YOUR SHOULDER ALIGNMENT OFF AND THUS THE DOG'S POSITION WILL BE OFF. Rather keep your focus just in front of your shoes, and if the dog is in position you should just be able to see its eyes. The use of mirrors is also very useful in watching your dog to assure they are in the correct position. You should also begin to measure the dog's position by the feel and action of the leash.
Next come the square corners. This may be something you want to practice without the dog to make sure you can do the same thing every time. Remember you do no want a marching or military square corner, but a natural walking square corner. And you want to do it the same way every time. For right turns, you want to plant your right foot, and then take a half step to the right with your left foot (heel to toe) and then step out with your right foot. This makes a nice smooth corner that is easy for the dog to follow and keep up with. About turns are the hardest as you want to make sure that you do not step out and into your dog, forcing it out of alignment. A good exercise is to practice this without your dog in a parking lot using the lines for guides. Your left foot should start on the line before the about turn and end on the line after the about turn. Not as easy as it sounds, hence the reason to practice it without the dog before you begin to teach it.
As with the others, I rarely do much off lead heeling except for at the trials or matches. And for matches, I generally use a shark line (a braided 4' boot lace attached to a small light weight clasp). Enter the match with both regular leash and shark line attached to collar. When in the ring, remove the leash while holding on to the shark line. This way you still have control of the dog and can give a correction if needed. Also patterns the dog to believe that even after you remove the leash you have control.
Also, remember that for a fast, you do not have to go full out! All that is required is an increased speed such that there is a noticeable increase in the dog's gait. Likewise on the figure eights, you want to keep your gait consistent while the dog's gait increases on the outside portion of the figure eight and decreases on the inside portion.
T. Mac