I'm 13 and have begun to write a book. I really want to publish it when it's done. I have been sending bits to my friends and they are enjoying their daily updates. If I went to my local library would they be able to help me find a publisher and give me advice?
Yes, snd no. Your local librarian will show you which books and databases contain the addresses of agents and publishers, but he or she will not help you approach the publishers.
You will also find a lot of information on this site about preparing a query, contacting an agent, and getting published.
Before all that, however, it's also a good idea to learn about the craft of writing. It troubles me that so many people want to know how to publish before they have learned how to write well.
At your age, no one wants to discourage you. Everyone wants to encourage young talent. But somewhere in there, it's also important to learn about the reality of writing and publishing.
Those seriously interested in writing have a great deal to learn and a lot of practice ahead of them.
I'm very much in favour of young people writing and publishing, but if you're interested in writing something lasting, I encourage you to spend as much time as possible learning about the craft of writing.
Take writing courses. Read books about writing. Have a professional writer comment on your work. And also do what you're doing--just write.
Learning about craft will make you stand out amongst others who have not yet taken the time to do so.