Below is my own (biased) advice on what makes a graduate student successful in their academic career.
Collect information. You are born the smartest and most creative you will ever be. To be effective, though, you need to learn how to channel your intelligence, and you need to provide your brain with information that it can use and combine in new ways. You should constantly add to the information in your brain, not only from scientific papers in your own research areas, but also from other fields, popular culture, etc. You never know which seemingly irrelevant tidbit will allow you to make your next discovery.
Be curious. This is related to the point above. Never leave questions unanswered—if you see a word you don’t understand, research it, if you hear about a new concept or technology, spend some time to better understand it. Also learn about other cultures, customs, religions, etc. All of this will make you more effective in research and also in interacting with others—a big part of everything you’ll do in your life.
Be coachable. When receiving advice or criticism, take it as an opportunity to improve, rather than an attack on your abilities. Never be defensive. Even if the criticism may be unfounded, you probably have not presented your ideas clearly enough, or have not argued your point effectively. There is always room to improve, and any feedback you receive allows you to do so. For the most part, people will provide criticism because they think it will help you grow. Be worried if you don’t get criticized—you may be pegged as a “lost cause”.
Actively seek feedback. Share ideas, paper drafts, etc. with others and seek their feedback. Specifically ask for constructive criticism. Beware the all too usual “this looks good to me”. Such feedback may boost your ego but will not help you improve.
Be humble. This is related to the earlier two points. Be aware of your limitations, inexperience, and general lack of knowledge. Cultivating such an attitude creates the environment for growth.
Read, read, read. Take the opportunity to read as much as you can. Not just science, but also literature of different types, pulp fiction, etc. This will help you communicate better both verbally and in writing. You’ll learn different ways of structuring arguments, phrasing ideas, etc.
Write, write, write. Take any opportunity you have to write. Papers, essays, reports, etc.—it doesn’t matter. It’s important that you constantly practice your writing skills. Use every email you write as an opportunity to practice. Re-read and revise your email before sending it on. Use complete sentences and well structured ideas.
Speak, speak, speak. Take up opportunities to hone your verbal communication skills. Ask to speak in lab meetings. Sign up for research in progress seminars. Look for other opportunities, whether or not related to your science. Join “speech clubs” whether formal (such as Toastmasters) or informal.
Avoid/restrict social media. Twitter, in particular, is harmful to you, both due to the constant updates/interruptions, and due to the very bad example it sets for how one should communicate (I’m personally “peeved” when someone refers to me as @Mihai). If you use social media, restrict its use to a small window of time during the day. Keep as many long stretches of uninterrupted time for your own research as possible. While the ability to multi-task and juggle competing distractions may appear to be a valuable “skill”, this is guaranteed to destroy your ability to formulate creative and innovative research ideas.
Have a hobby. Graduate school (and life) is hard and you’ll often encounter discouragement and emotional lows. You need to have something else to focus on in such times, allowing you to recharge your emotional batteries, and get yourself ready to go back to your research. Hobbies that allow you to demonstrate some kind of “achievement” are particularly useful, whether it’s finishing a 10 mile run, or learning how to play a song on your guitar, or cook a new dish, etc. Once you are done taking classes, progress is no longer easily quantified, especially as research often seems to run into dead ends. It’s important to find a way to give yourself small success stories that keep you motivated to continue this arduous journey.
Have fun. Try to enjoy research and life as much as possible. Keep a positive attitude and try not to dwell on the past, but look forward to a better future.