The transport of thermal plasma and fast ions in electrostatic microturbulence is studied. Strong density and potential fluctuations (delta n/n similar to delta phi/kT(e) similar to 0.5, f similar to 5-50 kHz) are observed in the large plasma device (LAPD) [W. Gekelman, H. Pfister, Z. Lucky et al., Rev. Sci. Instrum. 62, 2875 (1991)] in density gradient regions produced by obstacles with slab or cylindrical geometry. Wave characteristics and the associated plasma transport are modified by driving sheared E x B drift through biasing the obstacle and by modification of the axial magnetic fields (B-z) and the plasma species. Cross-field plasma transport is suppressed with small bias and large B-z and is enhanced with large bias and small B-z. The transition in thermal plasma confinement is well explained by the cross-phase between density and potential fluctuations. Large gyroradius lithium fast ion beam (rho(fast)/rho(s) similar to 10) orbits through the turbulent region. Scans with a collimated analyzer give detailed profiles of the fast ion spatial-temporal distribution. Fast-ion transport decreases rapidly with increasing fast-ion energy and gyroradius. Background waves with different scale lengths also alter the fast ion transport. Experimental results agree well with gyro-averaging theory. When the fast ion interacts with the wave for most of a wave period, a transition from super-diffusive to sub-diffusive transport is observed, as predicted by diffusion theory. Besides turbulent-wave-induced fast-ion transport, the static radial electric field (E-r) from biasing the obstacle leads to drift of the fast-ion beam centroid. The drift and broadening of the beam due to static E-r are evaluated both analytically and numerically. Simulation results indicate that the E-r induced transport is predominately convective. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.3695341]