We present a methodological approach, called Group Informatics, for understanding the social connections that are created between members of technologically mediated groups. Our methodological approach supports focused thinking about how online groups differ from each other, and diverge from their face-to-face counterparts. Group Informatics is grounded in 5 years of empirical studies of technologically mediated groups in online learning, software engineering, online political discourse, crisis informatics, and other domains. We describe the Group Informatics model and the related, 2-phase methodological approach in detail. Phase one of the methodological approach centers on a set of guiding research questions aimed at directing the application of Group Informatics to new corpora of integrated electronic trace data and qualitative research data. Phase 2 of the methodological approach is a systematic set of steps for transforming electronic trace data into weighted social networks.