We present a method for detection and reconstruction of the gravitational wave (GW) transients with the networks of advanced detectors. Originally designed to search for transients with the initial GW detectors, it uses significantly improved algorithms, which enhance both the low-latency searches with rapid localization of GW events for the electromagnetic follow-up and high confidence detection of a broad range of the transient GW sources. In this paper, we present the analytic framework of the method. Following a short description of the core analysis algorithms, we introduce a novel approach to the reconstruction of the GW polarization from a pattern of detector responses to a GW signal. This polarization pattern is a unique signature of an arbitrary GW signal that can be measured independently from the other source parameters. The polarization measurements enable rapid reconstruction of the GW waveforms, sky localization, and helps identification of the source origin.