The force on one charged particle due to a uniform magnetic field is $F=qvB\sin\theta$. According to this formula, the faster the particle's velocity, the greater the force of the magnetic field is going to exert on the particle. However, how does the magnetic field know how fast the particle is moving?
Fields don't "know" anything. "Knowing" is a anthropomorphic concept, based around how humans believe they operate.
The effects of a magnetic field on a charged particle are proportional to the derivative of position with respect to time. This is simply the equation used to predict the effects a magnetic field has.
Perhaps even more interesting is the Coriolis effect. The Coriolis effect fields a pseudo-force which is a function of the velocity of a particle. This is true, even though the Coriolis effect is merely an effect of viewing the trajectory of a particle in a rotating reference frame -- there is nothing physical to which we could even attribute its effects.