Speed improves through maximum-intent sprinting, strength that lets you apply more force to the ground, and better technique. Sprint fresh, keep the volume low and the quality high, take long rests, and combine it with heavy strength and plyometric work.
No amount of squatting or conditioning substitutes for actual high-speed running. Top speed is a specific skill, expressed at ground contact times of roughly a tenth of a second, and the only way to train that is to run at or near your maximum. Two short sprint sessions a week is enough for most athletes.
Sprinting is about applying large forces to the ground very quickly. Back squats, hip thrusts, and Nordic hamstring curls build the force capability, while pogo hops, bounding, and broad jumps train the fast expression of it.
The first 10 to 20 metres are about horizontal force production against a forward body lean, trained with sled pushes, falling starts, and wall drills. Maximum velocity is about vertical force in very short contacts, trained with flying sprints. Most field-sport athletes get more from acceleration work.
Sprinting is the highest-risk activity most athletes do, and hamstring strains are common when high-speed exposure is sudden. Reintroduce sprinting gradually after a break, always warm up thoroughly, and never sprint at maximum on tired legs.
Top speed is one of the harder qualities to improve, and gains are measured in fractions of a second over months. Acceleration and technique usually respond faster. See Sprint Mechanics and Maximum Velocity.