  Transition metal dichalcogenide (TMD) moir\'e heterostructures provide an
ideal platform to explore the extended Hubbard model1 where long-range Coulomb
interactions play a critical role in determining strongly correlated electron
states. This has led to experimental observations of Mott insulator states at
half filling2-4 as well as a variety of extended Wigner crystal states at
different fractional fillings5-9. Microscopic understanding of these emerging
quantum phases, however, is still lacking. Here we describe a novel scanning
tunneling microscopy (STM) technique for local sensing and manipulation of
correlated electrons in a gated WS2/WSe2 moir\'e superlattice that enables
experimental extraction of fundamental extended Hubbard model parameters. We
demonstrate that the charge state of local moir\'e sites can be imaged by their
influence on STM tunneling current, analogous to the charge-sensing mechanism
in a single-electron transistor. In addition to imaging, we are also able to
manipulate the charge state of correlated electrons. Discharge cascades of
correlated electrons in the moir\'e superlattice are locally induced by ramping
the STM bias, thus enabling the nearest-neighbor Coulomb interaction (UNN) to
be estimated. 2D mapping of the moir\'e electron charge states also enables us
to determine onsite energy fluctuations at different moir\'e sites. Our
technique should be broadly applicable to many semiconductor moir\'e systems,
offering a powerful new tool for microscopic characterization and control of
strongly correlated states in moir\'e superlattices.
