I have taught *lots* of kids to ride a bike. Maybe several dozen? I've lost count. Here's my method:
Take off the training wheels. Now. The only thing training wheels are useful for is learning how to pedal, and tricycles are better for that. Training wheels are actually counterproductive. They make the bike less stable. They make it impossible to lean into turns correctly. They teach bad starting and stopping habits. Get a really big tricycle if you like, but don't use training wheels.
Make sure the bike is the right size and setting for learning. The child's feet need to be flat on the ground when they are sitting on the seat. This is very low for an experienced rider, just right for a learner.
Remove the pedals. A bike shop can help you with this if you need help.
Note: I've had several kids call me lots of bad names when I took their training wheels and their pedals. They were all riding independently within a week, and were glad. Trust the process and feel free to ignore irate children.
Let the child use the bike as a kick-bike for a while. When you notice them going quite fast, doing long swoops and glides, they're ready to have their pedals back. For some kids this takes a day. For other kids, it takes months. Give lots of practice and be patient.
Put the pedals back on. A bike shop can help you if you need help. Follow teaching instructions below. From this point to solo riding takes anywhere from 10 minutes to a couple days, depending on the kid.
Have the kid get onto the bike and put their feet on the pedals, with you stabilizing the bike. Walk the bike around, with their feet on the pedals. Do lots of swoops, to show them how to lean into turns. Go over rough ground, up and down hills. My dad used to run me up and down drainage ditches. Remind them to move with the bike instead of fighting it.
Move to a long stretch of level pavement with few or no cars. A closed parking lot works well. So does a dead-end road. You want something that is fairly wide, since new riders are not the best at steering.
Hold onto their body, *not* the bike. The deal is this: they control the bike, you control their body. The bike might crash. They won't. If the bike is about to crash, simply lift them off the bike. Then, go retrieve the crashed bike and try again. This takes a lot of the fear out of learning. My students *never* crash while learning. Never. No scrapes, no injuries, no bruises. That's a promise that takes a lot of the fear out of learning.
The first step is just propelling the bike without falling over. Help them with starting and stopping. Remind them that it is much easier to balance a medium fast bike than a slow bike. Run alongside holding their body. Move to a looser grip when they seem ready, then to just a grip on their shirt. Don't let go. You promised not to. Keep that promise.
The next step is teaching the child to stop. They need to stop and *immediately* put a foot down. Go over this repeatedly until it's in muscle memory. If they fail to put a foot down, let them fall partway but catch them before they hit the ground. The feeling of falling will help them remember to put down a foot. Actually hitting the ground will just scare and injure them.
The next step is teaching the child to turn. Remind them that turning a bike is mostly done by leaning, with very little action in the handlebars. Start them on a straight, have them do a wide U-turn, then bike back.
The final step is teaching them to start. Help them get the pedal into the right starting position (about 3/4 of the way up). Start with the pedal on their dominant foot side. This would be the same foot as they use for kicking a ball. One foot on the ground, one foot on the pedal. Remind them to push down *hard*, and get the other foot on a pedal and start pedalling immediately. Then hold their body lightly and let them work on this. Let them fall partway to develop muscle memory, but don't let them hit the ground. It may take dozens of repetitions before they get it.
Expect that their steering will be terrible, so leave plenty of room for erratic steering. Remind them to look where they are going, rather than at their feet. This will help them keep balance and improve steering.
After they've got all four pieces (straight riding, turns, starting, stopping), you can work on some refinement. Have them turn around an object. Stop on a line. Remind them that a good stop has no skid. Skidding is losing control, and that is bad at this level. Work on control. If your child frequently rides on dirt,gravel, sand, or grass, this is a good time to talk about traction and how that effects turns. Tight turns on concrete is fine. Tight turns on gravel usually end badly.
So, now your child has all the pieces of bike riding. Have them do a few runs where you are just spotting them. Keep a light grip on their body and/or their shirt. Do not support them. You are just the emergency ejection system. It is their job to start, ride straight, and stop. When they get the hang of that, have them do a long oval. Start, right straight, turn, ride straight, stop.
At this point they will probably be feeling pretty confident and also somewhat irritated that they can't ride faster than you can run. When they feel they are ready for a solo, let them go for it. Some kids also like help with starting, but a ready to solo once the bike is rolling. In any case, make sure they know they are riding solo and feel ready for it.
You now have a kid on two wheels!
Warning: None of my students have crashed during the learning process. They all have a pretty spectacular wipeout 2-3 weeks later when they get overconfident and discover the limits of their abilities. I tell them all that this is coming. They all think it won't happen to them. They all do it anyway. Have bandages and antibiotic cream on hand.
Have fun!