I'll echo some points Tara already made.
- Books: Everybody Writes, Elements of Style, On Writing Well
- College: English, Comms, or (my recommendation) Journalism. I mention journalism because it gives you practical experience writing in comprehensive, plainspoken words while combining elements of user research + psychology and lets you work on interacting with many people from all walks of life. Being able to talk with anyone you meet is a wonderful skill for a writer. You'll find that the more people you meet, the more people will bring stories and inspiration to you.
- Craft: practice! Like Tara already mentioned, "write, write, write." Try joining a literary slam or quake or starting / collaborating on a 'zine.
Now I'll take some time to answer your specific questions.
What do I all need to do to become a writer? Answer: just a good attitude, knowledge of writing, honestly, and an audience.
What kind of classes will I need to take? Answer: some craft-focused stuff (literature, composition) and some inspiration-focused stuff, whatever you're interested in writing about!
When should I start checking on what I need to do? Answer: earlier is always better.
How long will it take to go to school? Answer: many writers I know never went to school. If you want to make a profession out of it, though, school can certainly help your resume stand out among others.
Consider a Bachelor's degree in English, Journalism, or Creative Writing: Although not required, a degree in a related field can give you a solid foundation in writing skills and techniques, as well as exposure to different types of writing. Take writing courses and workshops: Even if you don't pursue a degree, taking writing classes and attending workshops can help you improve your skills and build a portfolio of work. Build a portfolio of work: Start writing as soon as possible and build a portfolio of your best work. This can include articles, essays, short stories, and other pieces. Network with other writers: Join writing groups, attend conferences, and connect with other writers to learn from their experiences and get advice on breaking into the industry.
First and foremost, to become a writer you must write. All the time. For yourself and for others. Learn as much as you can about writing. Try different genres to learn which one speaks to your natural style. If you are in middle school or high school right now, take all the English or writing classes that you can - even poetry or script writing. Get engaged in writing and get engaged of the process of editing and getting feedback. One of the best things that I did for my writing was take a journalism class in high school where we published a monthly newsletter. The rigor of writing on a deadline can be very educational.
As for school, I assume that you mean college. Again, English class can be a powerful opportunity. You have the challenge in college of choosing what you want to focus on, such as journalism, screen writing, creative writing. I would say that it is never too early to be thinking about what you want to focus on if something comes to mind. I started college with a journalism major, before I realized that program was very competitive at the school that I applied to and I was just not competitive enough to do it. Looking back, I would have just focused on English and focused on getting my diploma as quickly as possible. The few writers that I know did not earn writing degrees in college. They studied other subjects that they then wrote about.
You can go to community college or a 4-year university and major in something directly related to writing. This can be Creative Writing, Journalism, English, Screenwriting, Communications, etc. This gives you the very valuable gift of time to dedicate to that craft. It helps you build up your networks early with classmates, professors, and working professionals. It also provides you with support and infrastructure to break into the field via student fellowships, grants, and internships. Most people begin applying to schools in the summer before their senior year of high-school throughout that fall semester. It's a good idea to asl for recommendation letters from your teachers or other supervisors/mentors earlier than that so they have time to write you a good letter. Especially if you intend to go into an arts program, many colleges ask for a writing sample(s) in addition to your standard college application essay. So it's good to have a nice portfolio of work. If you can, try taking creative writing or journalism classes and workshops while in high school. There are also very many programs for high school age writers such as YoungArts, Sundance writers fellowship, and Sewanee young writers conference that help you build your portfolio, hone your craft, look good on your resume, and help you network with other writers. You should also research to see if there are any writing groups/clubs in your area that you can join. Submittable is also a great website to search for writing opportunities for young people.
Let's say you decide against majoring in a writing-centric job. I would still suggest all of the above in terms of preparing for applications and networking with fellow writers. Many people major in related fields such as marketing. Another option is to minor in some type of writing while majoring in a separate field. Many people do this because it gives them a more financially secure place and broader reach in the job market. Here, it's still a good idea to hone your craft and build your portfolio of work. The difference is that it will be a bit tougher to carve out time to do it if it's not the core of your coursework.
Take your time when researching the various universities and colleges, and be sure to always keep your budget in mind. The times are tough and they aren't showing signs of getting better, so don't jump the gun and go to an expensive college or university just because it's the first enticing option you see.