I have a young horse who is working on this right now too, but my trainer is doing more of the work than I am right now :) But I'm going to tell you what my trainer (and other educated horsepeople) have taught me about this.
First, you need to develop a forward horse. Your horse should always be working with purpose, whether at the walk, trot, canter, whatever. That doesn't mean jigging or being too forward, but they shouldn't be lagging behind the motion.
Then, you want to develop a firm outside rein. When you are asking, you need to be more firm with the outside rein, and when the horse obeys, you will slightly soften but not completely. Basically you should always have some pressure on the outside. Then, the inside is what you use to ask. You are going to have light pressure and "sponge squeeze" gently with the inside rein to ask.
Make sure that while you are doing this, you are using proper hand position. My trainer compares it to and imaginary box above the withers, or you can ride with your hands lower on the side of the horse's withers while training instead of above the withers, depending on how your horse responds for the purpose of training and learning how to do this.
Lunging with side reins and a bridle is absolutely helpful in this. It's what I've been doing and it helps so much. Even 10 minutes (5 minutes each way on a really large circle) before each ride or workout is extremely helpful, and you can tighten the side reins and your horse progresses in his or her training.
Good luck, Happy Easter, & God bless.