I'm not exactly sure I understand the question. If you are asking how to relate to them, then the first key is understanding them.
You must know your demographic personally. Things such as socioeconomics, ethnicity, religion, politics, are all important. Having an understanding of your community's demographics can gain you insight into your consumer base's values, spending habits and needs.
Most consumers enjoy a business that can successfully blend professionalism with a personal approach to operations. To me, that means being able to be personal without being intrusive, and being knowledgable, resourceful and honest.
Now, if you are talking about interacting socially (as in socializing) with your client base. That's a completely different ballgame. That would entail becoming involved in the community in a credible way by demonstrating a sense of social responsibility. That may mean sponsoring charities by donating goods and services, organizing fundraisers, and so forth.