The chemical properties of atoms, molecules and of more complex systems such as clusters, nanoparticles or condensed matter systems are determined by valence electrons. Real-time control of these properties requires the capability of tracing as well as of driving valence electrons on their native temporal scale of motion, that is, within tens to thousands of attoseconds. Here we detail the technique of attosecond transient absorption spectroscopy. It combines the extreme sensitivity of core-level spectroscopy with the unprecedented temporal resolution offered by the tools of attosecond technology. We use the technique to demonstrate real-time tracing and complete characterization of coherent electron motion triggered by single, double or multiple ionization of atoms exposed to intense, few-cycle pulses. Our work opens the door to high fidelity, time-domain studies and control of electron dynamics in the microcosm.