Assuming that you're using 'office administrator' to mean the same as PA, that is, without specialist skills but a general helper and emergency substitute, then you should concentrate on showing that you are:
Focused on what you're to do.
Cheerful in yourself, serious about the job.
Quick to learn the employer's ways of doing things.
Always ready to say yes.
Beware of going too far. The gopher's jobs are always longer and less rewarding than others', but that doesn't mean you should submit to abuse. You will probably be expected to work long hours, but don't drive yourself into the ground. You can't work flat out, be smart, AND turn in a twelve-hour day, day after day. You must learn to pace yourself, to get the job done when it's needed, to prioritise your workload. You will make mistakes. Don't dwell on them, do learn from them, be sure other people notice that you're getting better.
When you do something praiseworthy, be sure the news gets to a person who can do you some good. Not necessarily your boss, who told you to do the job, but someone else, who may be Gossip Central, or simply another department's hiring person.
Step one. Get to know all of the major players.
Who does what. You don't have to understand their function yet but you have to know the name and department.
Step two. Get to know the others of your same position. Find the one who is doing better or knows more about things than the others. Schedule a real meeting with that person to get on the fast track to understanding expectations.
Step three. Know that you are going to be doing more than your boss. You will be involved in projects and issues that are not just simple daily tasks. When you work, remember that these issues are your issues as much as your bosses.
Step four. Know your boss. You don't have to like him but know how to anticipate his next move. Know his key phrases. Know who he depends on in his group.
Step five. Be ready for reassignment to another group. That means that you need to work to understand the things that make you interchangeable. You should not care at all if one day you move somewhere else. It just means learning the names and functions again.
Step six. Learn how to praise people. Not your boss but those who work for him.
Step seven. Remember that no one thinks you are important except those who know business really well. If someone is spending more time with you than others are, it means that this person is going up. Don't push that person away.
Step eight. Take a billion classes. Your goal is to have experiences. You are not the idea person but you are the person who knows how to apply those ideas using the tools that you learned in classes.
Step nine. Customer service skills. This is the difference between Admin and Executive assistant. How to talk to someone so that you get what you want and they want to give it. Some may say that it is people skills but it is not. You will have to own the conversation, dismiss ideas that don't work for you, set guidelines, etc. Its not about making nice, it is about getting your agenda through.
Step ten. Manage others to get them to work on tasks that you have been assigned to do but that clearly rests in their work regime. Follow up with them. Report their status and give them credit. It is not work that is going to be a feather in your cap. It only frees you up so that you can do other work that will be a feather in your cap.