Have your 10 second introduction ready to go. Be ready to make a connection with someone at any time.
Get involved - volunteer for company or community activities. Relationships are best built in the "off times" - those times outside of the project or away from the deadline. "Off times" can include lunch time, that time right before a meeting starts or right after it ends, or at company or community activities.
Be a resource to others and use your network as a resource. If you can add value to someone else's work or help solve someone else's challenge, you become a resource...and then you gain access to others' resources.
Really get to know others - build the relationship by making real connections that involve trust, reciprocity and genuine caring. It is the personal connection that takes a relationship to the next level...to a place where your career interests and ambitions can be shared and acted upon.
Follow up and follow through. After you meet someone or collect a business card, send the person an email. If you say you are going to do something, do it.