Start testing things out on your own. Start a blog, help a friend out with their website. If you do some research and practice the learning you'll quickly gain experience.
Find a job in an agency or in-house that will help you grow. My advice is to find a place that is hands-on. Find a great manager who will invest in you.
Learn to code. Technical SEO is very important. If you think you'll enjoy that aspect, take the time to learn.
Many people in SEO don't know what they're talking about because they've never actually done the work themselves. Find a place where you can execute and follow up to see the results.