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!