Oindree's contribution:

1. mentally prepare to spend 60 hours a week doing homework, 20 hours for each core class

2. know that everyone else is struggling too, in some way or the other

3. for homework -- do the problems you can do by yourself first, get them out of the way, the ones you are not sure about, work as a group

4. go to office hours of the professors - even the really strict ones might actually be quite nice and helpful during office hours 

5. remember to eat, sleep and bathe

6. having a personal life also helps, as it can remind you that life has meaning outside of grad school (importance of supportive family / partner / cat / dog / non-school activity cannot be over-emphasized ) 

7. if you are a TA, it will help you do better, not worse, in your classes as teaching is a great way to learn. Also TA-ing forces you to have a more structured/constrained schedule for doing homework.