Forgive me for being wordy here...I was in college for 13 years (4 degrees) and taught college for 15 years. (Those timespans overlap). I have quite a bit to say on this topic after that much experience.
Learn to live Low on the Hog!
Know your budget and live within it. This habit will serve you well all your life.
If you can avoid loans, do so.
Live as simply and cheaply as possible. There's only so much you can do about the tuition and fees, but you can almost always find a cheaper living situation.
Cook rather than order in pizza everynight. A pizza every week or 2 ok...but not every night.
Get a job...or two.
Walk, ride a bike, take the bus. Cars cost gas, insurance, maintenance in addition to purchase cost and god help you if you get a car loan and pay interest. Then there are parking fees, parking tickets and much much more.
Use cash not credit. Cash never incurs interest charges.
Pass your classes the first time! (I used to teach and couldn't believe how many students spent an extra year in college due to retaking failed courses...cheaper to put out the effort, even get a tutor, the first time around.)
Take a full load of courses rather than the minimum to get your loans. Where I went for my bachelors, we paid the same tuition for 12 credits or more. One semester I took 24 credits, most semesters I took 18. If part-time is cheaper or works better, that can be a money saver too.
Test out of any courses you can. You get the credits for the cost of the test, often minimal sometimes free.
If your high school offers a program to take college courses while the school district pays...do it!
Think long and hard before going to a "for profit" institution.
Try to find friends who are also living Low-on-the-Hog so you don't feel pressured into expensive recreation or poor financial/educational choices.
Don't get a dog! (I did in grad school and it was a money sink...fewer rentals to choose from, boarding costs when out of town or paying to have the dog flown cargo, vet bills...but I still loved that dog!) If you really want to be around dogs, the local humane society will usually be thrilled to have a volunteer dog walker. Or offer your services as a dog sitter. A friend of mine pays a college student to come walk her dogs every day and she lets the student use her wifi and washing machine.
Skip the spring break trip to Cancun or where ever one goes now. It's expensive and you can end up with compromising photos on the internet that hurt job chances later.
Take care of your health. Even with access to student health services, getting sick is expensive. Eat something other than the peanuts they hand you with your beer and go to the counseling service if you are getting depressed.
Talk to your professors. They will write you letters of recommendation later, but only if they know who you are.
Be a psych experiment subject...back in my day, we got 5 to 20$ per session and the sessions were all benign. They asked questions or measured our response times.
Pay tuition and rent first, when you get your scholarships or loan payouts. I often paid 6 months of rent at a time and used that to negotiate money off the monthly rent. Landlords like having all the rent upfront rather than having to process it each month. I also rented exclusively from folks who owned only 1 or a few rentals, not giant corporations. By knowing my landlord personally I could also negotiate doing my own painting and maintenance for money off the rent. I still use these rental techniques.
If you pay for laundry, hang up your clothes. Dryers are expensive to use at the laundromat and wear your clothes out.
I saved a bundle by living off campus but I was in a smaller town, not NYC...always check the rates. If your college requires you to live on campus and you believe you'd be better off living off campus, you can try getting a note from a doctor or counselor stating reasons why it is better for you to live off campus.
Take advantage of free entertainment.
Check into the recreation center rental programs before purchasing recreation equipment like tents, canoes, sleeping bags, etc.
Work hard on the SAT and ACT! Doing well on those gets you scholarships and can get you in the honors program at college. Honors program students often get preference when registering for classes or have access to the best professors.
Apply for every scholarship you are eligible for. I once got 500$ from my home town...only 3 other people even knew about the scholarship and applied so we all got some money.
Figure out a 4 year course plan your first semester. Your advisor is there to help you do this. If you have a plan, know which courses to take, and what your areas of flexibility are (electives, minors, etc), you can almost always finish in 4 years rather than 5.
Know the job market before you apply and use that knowledge. If you want to work in a particular industry, see where most of the people in it graduated. If they all went to MIT, then go to MIT. If they went to Texas State U, then go to Texas State U.
Keep an eye on the job market while you are in college. Your advisors will do their best, but you are the one who needs the job when you get out.
Learn to write a complete sentence. I now have a job where I need to hire people. I can be very flexible about what they majored in, but if they can't write a coherent report, properly spelled and punctuated, and grammatically correct, then I do not hire them. Your boss is not your proofreader.
Start your resume when you start college and keep it updated. It's hard to reconstruct your work and activities for 4 or 5 years of college when you are graduating and desperate for a job. Keep track of clubs, activities, honors, scholarships, awards, majors, minors, jobs, skills, etc.
If you want to go overseas, this might be the time. Many colleges and universities offer exchange programs where you pay the tuition and room/board fee at your home institution, and live and take classes overseas. This is great for expensive locations like Tokyo, London, Paris. A few countries may have cheaper rates than you're paying here and you might be able to negotiate the cost if that is the case.
Finally, remember that you get out of it what you put into it. If you put in minimal effort, you get minimal education. If you put out lots of effort, you get a good education.