As someone who completed a four year degree at a private university this is how I would go back saving money if I could do it all over again.
1. Visit your schools financial aid department and find out about all the scholarships and grants your school provides to its own students. If you're eligible for any of them make sure you apply! Then branch out and discover as many scholarships as possible that are related to your major, related to your academic and extracurricular actives, related to your family's financial situation, and so forth.
2. Live off campus if possible. I found personally that it would have been a lot cheaper to live off campus in a cheap shared apartment. If it's possible for you to do this then you shouldn't have too much trouble finding a roommate that is also a student at your school looking to save money or have more freedom off campus at least. Or better yet, live at home with family if possible and commute. Yeah you might miss out on some college social actives but it will be worth it in the long run. (No paying for outrageous housing fees that include mandatory meal plans and the other built in costs for living on campus). A couple of thousand saved living frugally off campus helps.
3. Get a part-time job. At least during your vacations such as summer and Christmas break if you feel you need to focus on your studies.
4. Don't feel pressure to go straight through school. If you feel you need to take some time off to work and save money then do so! I would also advise taking on as many paid and non paid internships as possible so you have a better chance at landing a job before or soon after you graduate.
5. Don't but any of your books or supplies at your college bookstore if you can help it. It's always cheaper to purchase textbooks on websites like Amazon or Ebay. Buy the books used and when you're done sell them back to your schools bookstore or sell them back on Amazon or Ebay. I learned this my last year and a half of college. I would have saved a ton of money if I bought my books and supplies elsewhere.
Those are just a few money saving tips that I can think of off the top of my head. If you want more suggestions feel free to PM me.