Controlling AUVs can be challenging because of the effect of complex non-linear hydrodynamic forces acting on the robot, which are significant in water and cannot be ignored. The problem is exacerbated for small AUVs for which the dynamics can change significantly with payload changes and deployments under different hydrodynamic conditions. The common approach to AUV control is a combination of passive stabilization with added buoyancy on top and weights on the bottom, and a PID controller tuned for simple and smooth motion primitives. However, the approach comes at the cost of sluggish controls and often the need to re-tune controllers with configuration changes. In this paper, we propose a fast (trainable in minutes), reinforcement learning-based approach for full 6 degree of freedom (DOF) control of a thruster-driven AUVs, taking 6-DOF command-conditioned inputs direct to thruster outputs. We present a new, highly parallelized simulator for underwater vehicle dynamics. We demonstrate this approach through zero-shot sim-to-real (with no tuning) transfer onto a real AUV that produces comparable results to hand-tuned PID controllers. Furthermore, we show that domain randomization on the simulator produces policies that are robust to small variations in vehicle's physical parameters.