If you come from a limited financial background, that's no reason that you shouldn't go to college. In fact, the less financial support you have, the easier it may be to secure financial aid. Financial aid is only given out to the neediest students. That being said, there can be stiff competition for financial aid packages, so you should apply early.
If you are looking to save money on tuition, state schools are much cheaper overall than private schools–especially if you can prove residency. This is not true across the board, however. In special situations, you could potentially get a higher scholarship for a private university than financial aid at your local university. It's important to weigh all of your options. Obviously, the school with the lowest tuition is a good first bet, but there are other factors to consider as well.
A good financial aid or grant program should be able to help with tuition, room and board, and supplies. If the latter is not included, cut costs by buying and selling used textbooks. Room and board can be a huge chunk of expenses–if you can cut costs by living in a shared living space, instead of a dorm, this is recommended. The trade-off is that you will have to make your own meals, but you can save hundreds of dollars a month on rent.
Getting a job is an absolute necessity–and may be mandatory as part of your financial aid package. Many financial aid packages require that you get a job on campus–a sort of pay as you go student loan. This may be preferable to other types of student loans, as you won't be saddled with payments after you graduate. The problem is that your work study paycheck will go right back to the school, which doesn't provide money for other expenses.
Student loans are by far the most popular form of tuition payment: borrow now, pay later. If you get a job during the school year, much of your paycheck will be going in pocket. At the same time, it is important to start paying off your student loan early on. Defaulting on student loan payments after you graduate can have long-term consequences. As you are trying to get footing in the workforce, it can be difficult to have to spend a large chunk of your paycheck on loans.
All that said, there is no reason to not go to college just because your parents cannot afford it. They may be able to meet you halfway by fronting some of the money if you are able to find a loan from somewhere else. Even if they don't help out at all, you can still pay off tuition and other expenses through government loans, private grants, school scholarships, work study programs, and more.