In order of importance:
Figure out how your performance will be measured... get the explicit metrics and numbers.
Learn the core skills of your job. The things required to be seen as a dependable & reliable resource.
Nail your first 3 assignments, and over-communicate your progress to your boss as you work through each assignment. Ask for feedback at each step, and mostly listen & ask questions during the feedback.
Figure out how your assignments and role contribute to the overall company objective. This will help you begin to learn about how to make tradeoff decisions on how to spend your time.
Find someone just ahead of you in your tenure (1-2 years) and get them to show you how to be successful... an informal mentor.
Figure out how your boss is measured and what is the weakest part of their performance... by the end of month 6, you should find a way to contribute to that objective outside of your own personal responsibilities. This is very high
Leverage extra credit and will help differentiate you.
Meet and build rapport with the people in your org who you will depend upon. Do one nice thing for each of them... perhaps helping them on a project or just offering thanks and feedback for a job well done.
Spend time with your team out of work. Get to know them personally.
Learn to give the elevator pitch on the importance of your role, business unit strategy, and company mission. These things come in handy.
This question originally appeared on Quora: What are the most important things to do (accomplish) in the first 3 to 6 months in a new job?