While you might still be nailing down your own duties, it's also important to extend a hand when possible. 

If you know a co-worker could use your help tying up a few loose ends on a project, offer your services. This will provide you with a chance to work with someone new, as well as showcase your willingness and ability to work on a team.

Ask yourself what you must accomplish in your first three months, what you want to accomplish in the future, and how you plan to continually improve your efficiency. These are just a few questions to set you off in the right direction. 

Take both physical and mental notes on what goes on around you. 

While you're immersing yourself in the culture of the company, also familiarize yourself with some of the other norms. How does your boss react to certain things? What are the problems you can provide solutions to? Take a "fly on the wall" mentality while you're settling in to see how the company functions.

Fitting in at a new job often means observing the overall culture of the company and adapting. 

Openly embrace the culture of your new company by making the office norms your new habits.

After observing daily operations for a while, reach out to someone you admire within the company. Shoot them an email or stop by their office and share your interest in learning about — and from — their experiences.

Step out of your comfort zone and attempt to interact with everyone you work with. 

Introduce yourself and always accept happy hour invitations. These are the individuals who are likely to be your networking connections for years to come.