Liquid-liquid phase separation (LLPS) of proteins into concentrated microdroplets (also called coacervation) is a phenomenon that is increasingly recognized to occur in many biological processes, both inside and outside the cell. While it has been established that LLPS can be described as a spinodal decomposition leading to demixing of an initially homogeneous protein solution, little is known about the assembly pathways by which soluble proteins aggregate into dense microdroplets. Using recent developments in techniques enabling the observation of matter suspended in liquid by transmission electron microscopy, we observed how a model intrinsically disordered protein phase-separates in liquid environment. Our observations reveal the dynamic mechanisms by which soluble proteins self-organize into condensed microdroplets with nanoscale and millisecond space and time resolution, respectively. With this method, the nucleation and initial growth steps of LLPS could be captured, opening the door for a deeper understanding of biomacromolecular complexes exhibiting LLPS ability.