We present results from a high-resolution spectroscopic survey of 45 L dwarfs, which includes both very low mass stars and brown dwarfs. Our spectra allow us to derive a significant number of new rotational velocities, and discover a slowly rotating (in projected velocity) L dwarf that allows more accurate measurement of spectroscopic rotations for these objects. We measure chromospheric activity (and often its variability) through the H alpha emission line. Our primary new result is good evidence that magnetic braking dominates the angular momentum evolution of even brown dwarfs, although spindown times appear to increase as mass decreases. We confirm that activity decreases as effective temperature decreases, although a larger fraction of L dwarfs are active than has previously been reported. Essentially all active objects are also variable. We confirm the lack of a rotation-activity connection for L dwarfs. We find a minimum limit for rotational velocities that increases with later spectral types, rising from near zero in older mid-M stars to more than 20 km s super(-1) for mid-L objects. There is strong evidence that all L dwarfs are rapid rotators. We derive a braking law that can depend on either temperature or mass which can explain all the rotational results and provides an age dependence for the angular momentum evolution. It is clear that angular momentum loss mechanisms in smaller and cooler objects become more inefficient, starting at the fully convective boundary.