Probably one of the most important things to do to save money (as a student, but also later in life) is to get into the habit of having a budget. You don't have to be too detailed about it, but without a budget it's incredibly easy to lose track of where all the money goes. Work out what you spend each week on things like food etc. Try to put some money away for major items like a car, travel, or even a house.
There are lots of apps out there that can be used to track your spending, I like the ones you can put on your 'phone as you can note things down as you spend rather than putting it in later (which can be forgotten), but a simple spreadsheet can work just as well. One app (free for android and iPhone) is https://www.moneysmart.gov.au/tools-and-resources/calculators-and-tools….
As you start to build up savings, think about putting the money into a managed fund (find a reputable one, but be careful that they don't have high fees) or even buying some shares. Many people have worked out it's better to buy shares in a bank, than to keep money in a bank account. Be aware of course that this is for long term saving - don't do that if you think you might want to access the money quickly.
Making both short as well as long term saving goals helps to make it all more enjoyable - so most important rule though, is set aside an amount for entertainment (food, parties, films, bands, etc) as taking a break from studying can help keep your mind fresh!