As Logan mentioned, I strongly advise considering a community college to get your associate's degree.
If there's a university you think you want to attend and it's in another state; attending a community college in that state can help you establish residency too. That way, when it's time to transfer to the university you'll have residency and won't have to pay out of state tuition. Some community colleges don't even charge out of state tuition too! That's what I did. I'm from California and wanted to go to Oregon. Went to a community college in Oregon, established residency and didn't have to pay any out of state tuition.
There are many ways. As mentioned by Pam, scholarships can help with this a lot. Do a lot of research and find as many scholarships you can fit the requirements for and apply to them. Often times there are lesser known ones that will have less applicants, which will improve your chances. You can also fill out FAFSA and apply for Federal Pell Grants. Another thing that can help is going to a community college to get your associate's degree before going to a university, as community colleges are often much cheaper. Picking a school that you can qualify for in-state tuition will help too.
This is how I was able to graduate college without debt. I started college at 21 after doing some volunteer work. I had about $5,000 saved up. I went to a private religious school that was very affordable, but still good quality. While I was in college I worked every semester, usually 20-30 hours a week. These were not high paying jobs, they were less than $1 above minimum wage. I didn't take full semester loads, I usually took 10-14 credits per semester, which helped me balance my work and school schedules. Then I would take summer classes or online classes to make up for the other credits, so I still finished in 4 years. I cooked and prepared all my meals instead of eating out (would eat out once per week). I lived with roommates to help make rent more affordable. I applied for federal pell grants and scholarships. My parents were not well off financially and I was always able to qualify for pell grants, which is great because you don't have to pay it back, it is free to you, just like a scholarship. Then as I progressed in college I was able to do a paid internship in my field of study, accounting. This internship paid well and helped me finish college debt free with a job offer in hand.
Graduating college debt free is not easy, it will take sacrifice and planning, but it can be done. It is a great goal, and will help give you a head start in your career as you will be used to balancing competing priorities and you can start saving with your first checks instead of paying off your loans. Graduating debt free might not work out for everyone that tries, but you can at least minimize the amount you go in to debt so will be easier to pay off later. Hope this helps, best of luck!
You'll need a plan and an early start on looking for scholarships in order to try to complete college debt free. You should have an idea of the field of study that you want to pursue and should narrow the colleges or universities that you want to attend. One source of aid can be found at the schools that you want to attend. Contact the both the financial aid office at the school and the department for the major that you are interested in studying and ask for a list of any merit or financial need based scholarships that are available to students. Other sources of financial aid include any professional association associated with your intended major or associations of which your parents are members. If you attend high school, your guidance counselor is a good resource to help look for financial aid for college.
Hope that helps.