I am a rising sophomore at a small LAC with a strong pre-med program. I went in my freshman year of college just looking to major in neuroscience, not really sure if I wanted to go to med school, but it is looking more and more appealing to me now. I did okay in my intro bio/chem courses that are required for the neuroscience major - they were the weed out courses for all science majors, and around half of the initial class dropped out - my grades could definitely have been worse, but could be better.
However, I was finding that I would be spending almost all my free time devoted to studying for my science classes, and was just about getting the same grades as classmates who didn’t spend as much time as I did getting work done. Any general tips for studying as a science major?? And additionally just any advice for a pre-med student (ex. studying for MCATs, summer/winter volunteer or shadow opportunities at hospitals (especially on the East coast))? I intend on reaching out to a couple professors this coming semester about doing research, so hopefully that goes well! 
In science class, you need to understand the CONCEPTS rather than memorize FACTS. Yes, some things you need to memorize such (Polyatomic ions in chem, the solubility rules).
For example, it is not enough to know “The electron affinity increases as you go right on the pereodic table.” You need to know the science behind concepts like these: “The electron affinity increases as you go right on the pereodic table BECAUSE as you move right the atomic radius decreases so the electrons are closer to the nucleus and will thus have stronger pull to the center.” Just memorizing how to solve a problem or memorixing facts will not help you truly grasp the concept.
In addition, HOW are you studying? Are you doing practice problems or Question/Answer, or are you just reading off your notes? I find that study methods-such as doing practice problems or quizzing/being quizzed by your friends- that force you to think and reason are very effective. Another tactic is to grab the dumbest kid in the class and ask him/her to study with you. Since he is a struggling student, you will pribably spend most of your time teaching him. That is what you WANT. Being able to teach someone else is among the highest levels of understanding. It will allow you to find your holes in your understanding and it will force you to explain the concepts at a fundamental level to allow your peer to understand them.
Also, I find that for science, high school preparation makes a big difference. For example, my high school has very good AP science classes; students who do well in AP chem/bio/physics at my school tend to crush intro science classes in college. You struggles in comparison to your classmates can just be because they had stronger preparation in high school.
As for volunteering opportunities, contact any doctor and ask them if they let students come in and shadow them. It doesn’t have to be a hospital; outpatient clinics often have less regulations on volunteers since they are small buisinesses, so it may be easier for you to get time to shadow. For research, try to get ahold of the professors at your school, and show sincere interest in the topics they are researching. Don’t just say ‘hey, do you have any research opportunities?’ Actully show interest in their projects. Additionally, asking them in person might be better since they are mroe likely to take you seriously if you go out and seek them rather than send an email.
Hope this helps!