Here are some tips to get you started on more productive walk work.
1. Connection. Take an even, soft connection on both reins with the hands a bit wide. You should have a direct line to the horse's mouth, meaning that neither rein should be touching the side of the horse's neck at this point. When you begin this exercise, you may open a can of worms right away because your horse may think that he doesn't want to face the bit at all. He may decide to make himself crooked and push one shoulder out. In that case, you may have the urge to use the rein to get him back in line, but it is better not to. Fix it with the leg by asking the horse to step to the rein straight, using your leg at the girth. Push the shoulders back in line and underneath the rein. The horse needs to accept the connection and be willing to go forward toward it in a relatively straight manner.
2. Flexion. Next, you need to define which is your inside rein and which is your outside rein by asking for a little bit of flexion. If you ask for right flexion, keep a soft connection on the left, apply your right leg at the girth and supple softly with your right hand. If the horse steps past your left rein and goes out his left shoulder you need to fix that with the leg. You may need to apply the right leg at the girth first, wait for your horse to start to step out and then apply the left leg, also forward, to remind your horse to connect and go toward the outside rein. So the sequence should be left contact, right leg at the girth, right suppling and positioning rein, left leg at the girth and then a receiving left hand. Be sure when your horse does give on the right that the flexion is at the poll and not just the base of his neck. Reverse everything for the other side.
3. Walk forward. Once you have a connection and flexion, you can ask him to walk forward with this feel. A rider should never pull the horse's head down with the hand. The horse will become round when he is connected and ahead-of-the-leg. Stay connected and make him walk to the bridle. Don't over bend his neck at the base because then the horse will start to fall out with his shoulder and lose everything. He should go freely forward with your allowing hand in the flexion that you create and he maintains. That is the big thing. If you feel that your horse is restrained, then it is most likely that you are restraining him. You need to kick him forward without restraining him. You don't have to say anything with your hand, you just need to stay connected and then follow him.
The horse needs to be in front of the leg with contact. Sometimes a horse will respond by breaking into a jog-like trot because for him it is better to trot behind the leg than walk connected and ahead of it. If this happens, you still have to keep the soft connection. The desired walk is on the other side of those jogging steps, not behind it. When a horse offers jog steps, often riders take their legs off and restrain the horse, therefore missing the opportunity to correct the problem. Your leg should ask the horse to get ahead of you and connect to the rein. If you try to walk a bit more and he trots, he still isn't really ahead of you. The horse has to accept and answer your leg pressure and go freely forward, unconstrained but connected to you.
If your horse swishes his tail and makes a face at you instead of complying, he is still behind the leg. The leg aid you need to put the horse in front of the leg is not a gouge with the spur. It is more a clap or a thump against the horse's sides with both legs, which recedes when you get the desired response.
During these exercises, you have to be careful to not contradict yourself by restraining with the hand, but you do need to keep the contact. Be sure you have the balance, skill and timing that you need in order to ride these exercises. Check that your horse is ahead of your leg many times each and every day. For example, everyone thinks about it in a walk-canter transition because that movement won't succeed if your horse is not ahead of you at that moment. Your walk should be like that all the time--always ready to canter, piaffe or anything you ask. Do not oppose yourself by asking your horse to go in front of the leg and then restraining him with a negative contact. If there is air in the rein, that's an invitation for the horse to be crooked or stop moving ahead of the leg.