Volunteer for a non-profit: One way you can use your writing for good is to volunteer to write for a non-profit organization. Pick a charity that is in need of help and offer your writing abilities. You can write newsletters, help with marketing materials or do grant writing.
Write articles: Write articles to publicize issues you are passionate about. Bring attention to these important issues by releasing well-written articles. You can publish these articles in the form of a blog or find a magazine that will publish them. Either way you are bringing light to something that is important to you.
Write a book: Another way you can use your writing to help a good cause is by writing a book and giving part of the proceeds to charity. Partner with a charity you care about and establish how much of the profits from your book will go toward this charity. As an added bonus, that charity will most likely advertise your book as well, which means more advertising and hopefully more sales.
Writers can make a difference, so if you want to change the world all you have to do is start writing.