Where do they come from?
When a boy gluon and a girl gluon hate each other very much a bouncing baby quark can form. Effectively the binding force increase to the point where quark creation can occur.
Ultimately, they appear to be fundamental particles that emerged out of the very early expansion of the universe as the fundamental forces differentiated.
Like any other particle, there are various processes that produce quarks at sufficiently high energy; the only real obstacles are a handful of conserved quantities (energy, charge, etc.). Hadronization, as well as the large mass and very short lifetime of the heavier quarks, makes it difficult to observe quark production directly.
Since it’s a common misconception, I’ll also point out here that quarks don’t form particles in the same way that atoms form molecules. For example, the flavor of a quark is not immutable; the weak interaction can convert quarks of one flavor to another. This is exactly what happens in beta decay, for instance. At the atomic level, the process looks like n -> p[sup]+[/sup] + e[sup]-[/sup] + ν; at the quark level, it looks like (ud)d -> (ud)u + W[sup]-[/sup] -> (ud)u + W[sup]-[/sup] + e[sup]-[/sup] + ν. The down quark just becomes an up quark. For that matter, the Z particle (basically equivalent to the W boson above, but with charge 0) can decay into a quark and antiquark. It’s not like the two quarks were hanging around inside the Z particle beforehand; the Z just spontaneously decayed into them. The short answer to your question, then, is that particles are created and destroyed all the time, and there’s no ‘conservation of quarks’. Energy is conserved, but individual particles are not.
From ducks! And quarks don’t echo!
“Quark: The sound made by a durk.” - Science Made Stupid
From cows, usually, but I suppose goats would work too.
Oh please :rolleyes:
We’re not children, you don’t have to dumb it down for us. 
Is there a reason you ask about quarks in particular? Are you comfortable with where, say, electrons come from? 'Cause it’s the same idea for both.
The short answer: If one particle smacks into another particle with sufficient energy, new particles can be produced. Exactly what happens to the starting particles in the collision, what new particles get produced, and what happens to those as they leave the collision depends on the particle species involved and their energies (and some quantum mechanical randomness). Examples available upon request.
As a point of interest, quarks and antiquarks are produced or destroyed in equal numbers. The fact that we have a universe filled with quarks and (essentially) no antiquarks is an unsolved problem in physics (though we have some decent leads).