Yup, I agree with tinyliny here. You can use what AcinATX has said too. I usually use the latter at the beginning stages and move to what tinyliny said when the horse knows what is being asked and has had plenty of time to adjust.
You need to set a nice active walk as your horse's baseline, meaning that anytime (cooling down and warming up included) you are riding/ lunging, you keep that active walk. If your horse is allowed to walk slowly on the regular, then he is going to think that is what you are alright with. When giving him this correction, if he trots off, then that is actually okay right now. He has gone forward and that is essentially what you have asked of him. For him to understand that you only want a more forward walk, just ask for him to come back to a walk with your seat and rein (if needed) and give him lots of praise. If he slows, repeat the process. It's very important here that you release your leg when he responds by going forward, otherwise he can become desensitized to your leg if it is used all the time.
Additionally, I prefer to reinforce this by cutting the ride short after they go forward, so that I do not have to drill it into them. I do this for three reasons: (1) I want riding to remain fun for them, (2) I find it gives them incentive to respond quicker and (3) With corrections like these, you do run the risk of a lateral walk appearing, due to tension and rhythm loss. Lateral walks do not always happen with these corrections as long as you work equally on relaxation, but they can be a pain to fix when they do.
To differentiate between slowing and speeding up the pace of the walk, you can use exactly what AcinATX has said. Simultaneously, you can use your seat ( Talking with Your Seat
). Then, eventually you can switch that aid over to mostly seat and little/ no leg.