The passage of gravitational waves changes the arm lengths between corners of the LISA spacecraft formation. These changes are detected interferometrically and recorded as phase measurements. The time series are reduced to reveal several signal types. First, the strong periodic signals from all types of galactic binaries and any strong chirped signals are identified by template fitting, and removed. Then weak, periodic signals and poorly characterized signals (e.g., generic bursts) are searched for. Next, weak signals with complex waveforms, such as from compact objects orbiting massive black holes, are sought with templates. Genetic algorithms, template structure or hierarchical searches are used to efficiently search the very large parameter space. Finally, backgrounds from galactic binaries, extragalactic binaries and the Big Bang will/may be separable by their signatures.