1. You should no longer be aiming to be the best student in class. In fact, you probably won’t be the best student in class. You won’t be good at everything you do, in the lab or in the classroom. Work hard. Read. Ask questions. Be curious. Think outside the box. Don’t freak out if you don’t understand everything. Grad school is hard. Your classes are meant to provide a scaffold on which to grow as a researcher. They are NOT the most important things you will do as a grad student – your transcripts won’t be included in your postdoc or tenure-track job application.
2. Don’t compare yourself to others. I don’t care if Joe Blow in the lab next door had 5 Nature papers when he graduated. Having one or two good papers in high-profile journals is enough* to impress and find a good postdoc, even a great postdoc. The most important thing you need to do as a student is learn how to think, write, and talk about your science. Papers are important, but they shouldn’t be used as a comparison of how well you’re doing compared to your peers (even if YOU happen to be Joe Blow with 5 Nature papers). Your journey** as a grad student will be different than every one of your peers. You will struggle at things others find easy, and you’ll fly over hurdles that your peers can’t seem to crawl around. Keep your eye on the goal – your own goal. Don’t worry so much about everybody else.
*At least in my field; this is completely field and sub-field, even sub-sub-field specific, which is kind of the point here.
**Maybe the word “journey” is a little cheesy here, but I don’t really give a shit.