I start by getting them used to putting the board on and floating with it. I really emphasize to them the board floats and their life jacket will also keep them afloat even if they should go under water for a second.A pool is really best so they aren't intimidated by larger bodies of water, I have also done it at the lake plenty. I teach them to relax when they are floating and to save their energy until the rope starts to pull them.
Then I put the rope in their hands and gently pull the rope by hand . I tell them to bend their knees and try and keep their butts in the water (so they don't fall over the board). As I pull I tell them to push their feet towards me but don't stand up. They are so light they can actually practically get up. Once they are getting the hang of it I intentionally pull them over the board ends up behind them and they are floating on their stomachs. This usually scares the hell out of them and I want them to get used to the sensation and reinforce they are just find and floating. Usually they aren't sting enough to flip the board over by themselves so they may be in this position for a moment. I teach them to extend their bodies as long as possible and throw their elbow, shoulder, and hips back to roll the board over. I usually give them a little help to initiate the roll.
Every kid learns at a different pace. Be patient. Sometimes they just put the board on and don't even get in. Sometimes a few hand pulls and they are done. It's ok, if they do a little or a lot it's still progression. Some kids go an entire summer just doing the steps I listed and never get pulled by the boat. I don't care, I only push them as hard as they are willing to be pushed and want it to be a positive experience.
When they are ready for the boat your driving is huge. They need almost no pop so throttle to hard and you pull them over. To little and they drag undoubtably drinking lake water. Consistency is key. When you get it all together your four year old will be up and riding. Here's mine on a hyperlite motive 109.