I understand that the heavier quarks, charm/strange/top/bottom, are short lived and decay into other particles. But how are they "created" in the first place? Do other particles combine in a collision to create them somehow? I'm only assuming they are "created" because they decay so quickly.
In a particle collider (such as the Large Hadron Collider) a beam of charged particles (typically electrons or protons) is accelerated to relativistic speeds and then collided with either a stationary target or another beam of particles travelling in the opposite direction.
Some of the kinetic energy stored in the beams and released in the collision goes into the creation of new particles and antiparticles, which may include the heavier quarks. There are many different ways in which sufficiently energetic particles may react with one another via the strong force and the weak force to produce new particles/antiparticles.
They are "created" in the same way other quarks are: from vertices with gluons, Z and W bosons, or even photons.
It is the same thing with heavier leptons, like the muon: they are created from Z and W bosons and photons, and via the same particles they decay in lighter leptons, like the electron.