You have to be clever.
You can get momentum from a collision.
You can rig a detector to intercept part of a whole bunch of particles, then do it again in a different place, and use the time between them. You don't get the speed of the particular particles detected but you do get the speed of the bunch.
You can pass a beam through rotating collimators like you do to measure the speed of light.
Short answer: lots of ways.