The fact that you want to be the best is half the battle. Many residents just want to make it through, get a job and make a lot of money.
Remember you are a physician and not a technician. Baby Miller is a great place to start for learning the nuts and bolts about how anesthesia works but learning to be a good anesthesia physician is about seeing the big picture and not just Prope,Sux, Tube, Gas.
Things to do:
1) Read about the case before you do it, ask questions during and read again when you get home. Review the interesting comorbidities, medications the patient takes and why your attending chose one technique over another. This is easier when you see something interesting but should be done for most cases. You can do this before you leave work, read one chapter at home and spend the rest of the night goofing off.
2) Ask to do the biggest cases as soon as they will let you. Don't shy away because its scary. It is scary, but you have backup and you are there to learn.
3) Talk to the surgeons or surgical residents about the case. Pay attention to the field. Don't use your downtime in the OR to text your girlfriend.
4) Call is where you learn the most. Keep your eyes open and learn from your seniors.
5) Find the best attending in your program and copy them.
6) Know why you do everything. Knee-jerk reactions are for crnas. Labetalol is not always the answer.
7) In between cases, visit your co-residents. See what cases they are doing, have them teach you something. Ask why they are using one technique over the other. This is like multiplying your case numbers in half the time.
8) Run TO codes not away. If it looks handled, watch and learn.
9) Develop a few good shticks for getting kids to blow through that mask.
10) Clean, clear charting implies clean clear thinking.
11) Don't be cocky, they'll be people who will want to see you fail if you are.
12) I don't agree with the Ho recc. The book has a TON of errors since he never got it professionally edited. Same with Big Blue. Stick with the edited stuff. Worry about the boards later.