The most natural way to get to know people is to just let it happen organically. In an article at Business Insider, Lauren Dunn outlines some ways that you can build relationships without trying too hard.
For instance, small talk will go a long way. Just asking people about their weekend (etc.) on a regular basis will lead to learning a lot about each other over time. Avoid gossip and being overly negative, because such things are not productive. Maintain politeness at all times.
The only way in which you might need to “push along” relationships is if you are looking to network across departments, in which case, yes, you will have to hunt some people down in order to talk to them. For further discussion, you can view the original article here: http://www.businessinsider.com/how-to-get-to-know-your-co-workers-2013-6