  Quantum Monte Carlo methods have recently been employed to study properties
of nuclei and infinite matter using local chiral effective field theory
interactions. In this work, we present a detailed description of the auxiliary
field diffusion Monte Carlo algorithm for nuclei in combination with local
chiral two- and three-nucleon interactions up to next-to-next-to-leading order.
We show results for the binding energy, charge radius, charge form factor, and
Coulomb sum rule in nuclei with $3\le A\le16$. Particular attention is devoted
to the effect of different operator structures in the three-body force for
different cutoffs. The outcomes suggest that local chiral interactions fit to
few-body observables give a very good description of the ground-state
properties of nuclei up to $^{16}$O, with the exception of one fit for the
softer cutoff which predicts overbinding in larger nuclei.
