Once you have collected your data and put it in a matrix form, you can use a number of software tools to perform the analysis. This will allow you to track the flow of information, identify important actors, or detect communities within the network. You will be able to compute a number of local and network-level measures (transitivity, reciprocity, network density and centralization, among others). The analyses will inform your understanding about the structure of relationships between the members of your population of interest.
All of the programs mentioned here have detailed - and helpful! - online manuals.