There are several ways to analyze the network, depending on which is the question you are trying to answer. You can start using the Analyze Network tool included in Cytoscape, which provides basic analyses about network topology (degree distribution, betweenness centrality, etc..). Afterwards, you can use one of the several plug-ins (or Apps), to perform other specific analyses. One common thing people do, for example, is to search for subclusters of the network. So, to summarize, try to figure out what do you want to obtain from the network and "play" with it and the apps.