Like buying your first drill, or watching the school nativity play, this is one of the rites of passage of parenthood.
The practical stuff
Assuming, like me, you have never taken your child on long cycling holidays and got them riding those little bikes with trainer wheels up and down the local hills, you will have to start from scratch.
This means assuming your little darling is going to fall off. Thus, you will have to buy elbow and kneepads and gloves which protect her palms, while leaving the fingers free to operate the brakes. (Skateboarding shops sell better ones than bike shops)
You can get a helmet, but follow your own judgement on that (unless the law says otherwise—as it does in Australia, some US States and elsewhere). She might well feel more grown up in a helmet. Personally, I don't think it is necessary during this initial learning phase (but please don't sue me if she gets concussed). Once she knows how to ride, but is not yet completely at home on a bike, and as speeds increase, then I think a helmet becomes essential.
It means finding a bike which is the right size. That probably means one size smaller than you thought. It also means adjusting the saddle height so that she can sit comfortably on the saddle, with both feet flat on the ground. I mean flat on the ground.
Next, find a flat, paved area, ideally with grass to both sides. Remove any training wheels on the bike and get her to sit on the bike with hands on the handlebars, feet on the ground and start 'walking' it around. She should push the bike along using her feet against the ground. The pedals will get in the way, but that is part of the process.
Go in a straight line at first, and then start turning corners. At this point, if the saddle is too high, your child will let you know about it. Make sure she can place both feet flat on the ground. If this is her first time, she will almost certainly drop the bike when she starts turning a corner, and she will need a good firm stance on the ground to recover her balance.
When she can push the bike along like this, without dropping it too often, it is time to move up a gear. Find a road with a gentle slope (and more importantly no cars and few other cyclists, pedestrians/ bladers etc). The slope should be steep enough that when you push off while sitting on the bike, it will coast down the slope at more or less constant speed.
Get her to 'walk' the bike down the slope in the same way she was doing on the flat ground. Just walk it, nothing more. She may need to use the brakes at this point. When she can walk the bike down the hill, encourage her to lift her feet off the ground a bit, and let the bike coast along underneath her, with feet on either side to prevent falls. You might like to push her back up the hill as she rests her feet on the pedals.
Next step is to gradually extend the time she can coast with feet off the ground. At this stage (if not before), it is a good idea to encourage her to look where she is going. Maybe stand in the middle of the road and tell her to aim at you. Maybe run backwards at the same speed, so that she constantly has something to aim at.
If it helps here, you can measure the time she keeps her feet off the ground with a stopwatch, and get her to beat her own record. It has to be said, that the time might be only a second or two—or even less.
Some children can keep this up for an hour or more; others will want to stop after just a few runs. Try to make some sort of progress at each session, but also try to allow her to control the process as much as possible. This is largely about building her own self-confidence in her ability to control the bike, steer, and slow down all at the same time. If that means stopping after 10 runs and returning next day, or next week, that is OK. She'll be ready to take it further next time.
Once she is confident about the speed and steering and her ability to stop, encourage her to rest her feet on the pedals while coasting downhill. It may help if at the start of a run you hold the bike upright, get her to put her feet on the pedals and then push the bike up to (a slow coasting) speed before letting go and letting her coast down the slope. Once she is freewheeling, she can choose whether to carry on, or to use the brakes to stop.
At some point, she is going to lose control and have an accident. Hopefully, the speeds will be slow, and she will manage to half stop the bike before falling off, but those knee pads and elbow pads and gloves are wonderful. Even fragile youngsters will be able to get up unhurt and carry right on after a fall if the pads are fitted properly.
For my daughter, the biggest step was increasing the length of the freewheel. She got so excited about her ability to go for a few yards that she yelled out telling everyone in earshot to watch her, and then looked about for approval, making the bike go all wobbly which sent her into a panic. And then, she found it hard to relax and stiffened up, making her over-react when the bike went in the wrong direction.
Her face was flushed with pride and excitement, and she proudly described the sound of wind rushing in her ears. It is a big thing for a child to be going so fast under her own control and power. Don't rush her through it. Let her feel the speed and excitement and thrill of this wonderful experience.
At this point she decided it was time to stop and go for an ice cream. Next week I will try to extend the freewheel until she can go all the way down the hill—about 100 metres. Once she can do that, I think it is all over except for lots of practice. The final step of pushing on the pedals will be a small one by comparison.
Update: A week later, we spent another hour at the same hill in Richmond Park and after a couple more attempts at coasting, she was pedalling away with the best of them for a kilometre or more. She can ride her bike. Yay! Now it is just a question of getting more strength in the legs to go uphill, practising starting off and perfecting the steering and balance. Hey folks, it works! I estimate it took a total of three hours spread over three weeks. A lot of our friends used different methods, but in most cases, when the child was ready, it took just a few hours to learn.
Update 2: Another week on, she has been practising starting off in the backyard, and has progressed a lot as her muscles get used to the unfamilar movements. We also went back to Richmond Park. She is now cycling uphill quite confidently, but still sometimes finds steering a bit of a problem. She can reliably start off on a flat, paved surface, but has difficulty if the surface is rough or sloping uphill. Over the next few weeks we will increase the height of the saddle, as apparently, the low saddle can damage her knees.
Update , six months later: She rides very well now, and has progressed to a bigger bike. Yesterday we took our son (five years old)up to the same hill, and within an hour, he was cycling down the hill pushing the pedals around. Comment from an on-looker, "I think you've cracked it." And we had. he just needs a bit more practice, and he too will be able to cycle.
The emotional stuff.
I am thrilled and yet worried at the prospect of my daughter learning to ride her bike. Thrilled because she is learning to become more independent; able to travel faster and further than ever before under her own control.
Worried for exactly the same reasons. She is growing up. Before school, she learned most of her language and culture from us, her parents. Now, at school, she learns from the more knowing kids. She has never heard either of their parents say "fuck", yet now I sometimes hear her practicing how to say the word. She asks what it means and why her friend said it.
These are small issues: easy to deal with. And yet, a hundred small issues add up to something bigger: a growing gap between what we can offer her and what she wants. Between what we do together as a family and what she wants to do for herself.
She is eight. She is not a natural ballerina. Her friends have been riding their bikes for some years now, and we finally decided it was time to teach her. I can see that she is growing apart: seeing things through her own eyes, creating her own experiences, and we decide that now is the time to give her more freedom than she has ever had.
Will I let her use that freedom? I don't know. I seem to have spent a lot of time recently trying to explain why she may not do some things, I need to tell her why I think it is a bad idea to go into town alone. I have to say there are bad people, that her body is her own and tell her how to defend herself and get out of trouble. I have to teach her the value of money and why it is not a good idea to give away the twenty given by a relative, just because her streetwise friend asked for it. I have to tell her that it is sometimes OK to just run away from people.
And yet I have to tell her that it is not OK to run away from me. And when I ask her to do something, she should do it straight away, unquestioning. It's tough, and she is having a tough time understanding where the limits lie and when she can step over them. She argues all the time, constantly testing me and my resolve. These issues are not new, but with bike riding, they take on an extra edge, because by teaching her to do this, I know I am going to have to rely much more on her own ability to make good decisions.