Well, the first thing to do, is ask questions. And be sure to take notes when you get the answers, so that you don't forget.
Consider this: your boss wants you to succeed. That makes her look good, and it saves her money. But you cannot succeed if you don't know what she wants from you.
Most bosses (and I had 2 bosses who were horrible people, so I can tell you for sure that there are occasional exceptions) welcome questions, so long as you don't keep asking the same questions over and over again. You want to show that you're paying attention and learning, right?
Here's what I do. First, I ask a colleague if they can help me. Now that I've been in this particular job for a year, I have a pretty good handle on who knows what, but if I am unsure, I will say, if you're not the right person, please direct me to the right one. Of course, you don't interrupt people who are very, very busy. You knock or clear your throat and ask if it's a good time. Sometimes it isn't, and people appreciate that a lot more than you just rushing in and bothering them.
If my colleague doesn't know, then I go to my boss. And I'll tell her, I asked E____ but she was busy or I asked B___ and he didn't know. And I have my pad of paper and pen and I take notes.
Our office happens to have a Wiki, which is an updatable website. I have taken it upon myself to document whatever I learn. And my boss loves it! What we do needs to be documented, and what better person to do that than the new gal?
If there isn't this kind of a system, you can also write up a Word document or an email with what you've learned. And then you can send it around once you think it's correct and complete and ask, do I have the methodology down? Am I missing or misstating anything?
The vast majority of places want you to succeed because when the team succeeds, everybody benefits. It'll be okay. Just ask, and chances are very good that someone in the office will be happy to help you -- and will be very glad that you asked.