How do I learn it? Can't I teach it myself? Are there books?
If you want to learn to play the clarinet - and more so if your daughter or son does - the most promising way is to find a good teacher and take lessons. Off course you can try to teach it yourself, and people say there are people who managed that, but I have never met one personally who succeeded. That doesn't mean it is impossible - you can even buy books on this.
NB.: I am neither a clarinet teacher nor a professional clarinettist. You will find that some of those do sometimes defend their opinions in a nearly fundamental way. All of these may have good reasons for their opinions. I will try to lay out what I found most usefull, especially when you read this thinking about whether your own children should learn the clarinet and how to proceed.
Learning to play a musical instrument like the clarinet is more than an intellectual process, that you may manage by abstract learning. It is like skiing, where nobody would try to buy a good book and then teach it himself - at least when you stand on a steep slope you'll find out quickly that was not such a good idea. Very much alike when learning to play the clarinet there are a lot of things (how to sit, hold the instrument, your embouchure, how to breathe and move relaxed, how to control a tone) to train simultaniously and these things ought to be checked.
The beginning can be difficult and you can do a lot of things really wrong (and get used to that). Especially for the first hours it is worth to have a good teacher.
If you want your child to learn playing the clarinet it is quite common to go and buy an instrument, then try to find a teacher. The other way round makes more sense: Find a good teacher, then, together with him or her go and lend an instrument and if everything goes well, maybe, you buy a good instrument maybe a year later.
Where do you find clarinet teachers?
This can be quite different depending on the country you live in and the music education system this country has. Some states do have state-owned music schools. In some states musical education is something public schools do, and then again it can be a private service - there are private music schools like Yamaha's and there are private teachers. Often music students and orchestra musicians give lessons, too.
Amateur bands and orchestras often have startup bands and organise their own teaching, at least they can help you to find a good teacher.
Music shops should be able to help you, too.
What do you look for in a good clarinet teacher?
Off course you should have a serious talk with that person, especially when it is not you but your child who will be learning the clarinet - the kid will spend a lot of time with the instrument and the impact a gifted or bad teacher can have can hardly be exaggerated. Especially for kids it is rather the didactical and motivational abilities the teacher has than the fact, that she or he is a great artist (plays in an excellent orchestra) - at least for the beginning that does not help you much. It is a good idea to talk to good amateur players around where they learnt their skills (you can find them at concertos of local orchestras or wind bands in your neighborhood).
If you or your child are not happy with the teacher (any more), just go there and talk about it, maybe cancel the contract and go find somebody better. Don't hang around for years with a teacher you don't like simply because you once started with her or him.
In the beginning: slowly!
Of course a beginner wants to know how to play the whole tone range - the upper registers, too. But the teacher should, as long as he or she is good, hold the beginner back. There is enough to study in the Chalumeau register and there are some problems to overcome and some bad habits to prevent. This phase should take some weeks - and it is proven to be the best way for most people! Once the first steps are mastered fully, you continue with the clarinet register, which is really tricky. It is rather a problem if your teacher is too fast here.
And: Of cours you can easily play fast runs on a clarinet, even a beginner can. If you want to play not only fast but precisely one day, you'd rather learn to practice extremely slowly. The teacher should enforce this as good as she or he can. If you don't see this happen, one should start to think about the teacher's qualities...
And after two years I can go it alone, right?
After two or three years you have learnt the basic technique and musical abilities that you will need for playing for example the third clarinet in a band, but still a teacher will make sense (maybe not on a weekly basis like for a beginner) in order to look at habits you develop and weaknesses you might overcome. This costs money, off course. You could have your own peer group of other clarinet players like in a clarinet quintet, where you meet frequently and rehearse together. But even professionals do go to a good teacher every now and then to get a direct and focused feedback.