Chronographs were used. The basic principle was to use some form of precise timer to measure how long it took the bullet to go a certain distance. Modern chronographs use very small distances (on the order of a foot or two), but older systems involved longer distances and lower precision.
Major General Julian S. Hatcher in his experiments in the interwar period with the Ordnance Department specifically mentions a "LeBoulonge Chronograph" that gives the velocity at 78 feet. The system involved a stop sensor at 156 feet, which, when dividing the distance (156 feet) by time it took to travel, provides an average velocity, which translates to roughly the velocity at 78 feet from the muzzle.
Other methods to measure velocity existed, however. The first such methods were momentum based - a bullet was fired at a pendulum, and the motion imparted on the pendulum could be used to calculate the momentum of the bullet, which then could be divided by the mass of the bullet to provide velocity on impact. Another method involved a spinning mechanism with a series of targets placed behind eachother. The rotational rate of the spinning table and velocity of the bullet would affect the impact points on the targets behind the first, and this could be used to calculate the velocity of the bullet.