Hopefully, as a graduate student in the sciences you have health insurance from your university. If your only source of income is your teaching appointment or your stipend, then you could qualify for medicaid, so be sure to get covered. Get your flu shot because catching the flu can cost you a lot in terms of your experimental time line. If you have insurance, you can usually get the flu shot for free or really cheap.
If you live within reasonable distance from the school, consider biking or walking to school for your daily exercise as opposed to paying for a gym membership. If you must work out in a gym (not knocking against it), shower at the gym to save on water costs at home.
Do NOT shop for fun. This will cause you to waste money on things you don’t need. Don’t sign up for free subscriptions if payment information is needed because cancellation can be a pain, and many will bill you automatically after the trial period has expired. If you like to tv, weigh the cost of cable tv service to a netflix subscription and choose carefully. You shouldn’t need both. If you like to hang out in bookstores and are the type that always ends up buying something, go to your campus library instead.
If you eat out a lot, look for coupons/discounts to your favorite restaurants. Assuming you are eating out with your friends for entertainment consider limiting your party to less than six people as many restaurants will automatically add a service charge when there are six or more people. Also consider potlucks and picnics as an alternative to eating out, especially if you rarely see the light of day.