To become a children's writer it is necessary to be patient and persistent when waiting to be published. Most children's writers have written a number of unpublished manuscripts, but they keep sending their work to literary agents or publishers. There are no specific educational requirements to become a children's writer, but many have pursued a four-year degree in English, or even a master's degree in creative writing.
There is no set formula to become a children's writer. Some writers will say that it is necessary to practice and write something every day, while others will say it is necessary to write only when the mood strikes. It is best to determine what works best for you. It is also necessary to determine what type of children's books you want to write. This may be books for very young preschool-age children, elementary or middle school kids, or even young adults.
Once you have written something that you believe could be published, it may be helpful to have other people read it before sending it anywhere for potential publication. A new set of eyes may be able to point out mistakes that can be corrected, or confusing areas to be clarified. By the same token, getting input from children could also be useful, since they are the audience you are really writing for. Once it is ready to be sent to publishers, it is necessary to thoroughly research children's book publishers to see where it is appropriate to send.
Children's book publishers have extremely stringent rules about accepting manuscripts from unpublished authors. Some will only accept a query letter, others will take a portion of the manuscript or the whole thing, while others won't accept unsolicited queries at all, and will only take manuscripts from literary agents. Follow the rules of each individual publisher to the letter, because those who don't follow the rules will simply have their work thrown out.
To become a children's writer it is not necessary to illustrate your own work. A publisher will likely have in-house or freelance illustrators to handle the illustrations; in fact, it can be more difficult to publish a children's book if you have illustrations that you insist must go along with it. If you are finding it impossible to become a children's writer through the avenues of book publishing, there are other areas to explore. Some children's writers begin by working as freelance contributors to children's magazines, by entering children's fiction contests, or even by contributing to websites for children. If one is determined to become a children's writer, there are many possibilities to explore.