If there was a book on Student Travel, the most read chapter would certainly be "How can a student Travel Cheap?".
Having worked in the travel industry for a number of years there are some standard know-hows that make travel cheap for students. The first is to travel in a group. Although you might not want group travel to cramp your style of searching for the truths of the universe, you will quickly realize a group trip is better than no trip. By the end of the trip you will learn a lot about yourself and that becoming an adult is mostly made up of meeting people, them getting on your nerves, then figuring out how to deal with them. So consider it an investment for the rest of life that you are actually saving money on. Group travel lowers the price on lodging, transportation, food, and any activities you sign up for.
Second way to travel cheap for students is to plan ahead. Do your research. I remember when I traveled as a student we would have everything planned out and seldom changed plans that would affect cost. Today I will admit I unfortunately loose money by simply changing plans on the fly and not really knowing where I am going only because $50 or $100 loss is not as tragic as it was 20 years ago. If you lose $100 on a student trip that could very likely be the difference between being stranded in Moroco for the rest of your life or arriving home on the dime for Thanksgiving dinner. Plan ahead and stay on track.
Finally and most important is do not treat it as your last trip. If you fall into the groove of, we are in Rome so we might as well eat and sleep fancy for the night then you will be broke quick. Chances are you have only been on the Earth for 18 to 25 years. I understand a big trip is a major event but you want to take it easy for two reasons. First, you want to feel like you have something to go back for. This will help you later on in life with motivation to take another trip. Second, some of the best moments on big trips are doing things that don't cost much money. Instead of the big expensive tours try for a more local gig. Look for local groups of any interest and just show up out of the blue.
Traveling cheap as a student is easier than you think and remember you are built like a modern day gladiator. At 19 years old you can eat, sleep, and enjoy pretty much anything so use that superpower to your advantage assuming you are safe.
If you have to splurge on something, don't be afraid to spend on water! Dehydration is the kryptonite of the youthful traveling gladiator. Stay hydrated even if it costs you!