What evidence is there of the existence of quarks?

What is the experimental evidence that suggests the existence of quarks?

It was a great time for experimentalists back in 1960 when the existence of quarks was first suspected.

How were they discovered?

It was called the eightfold way to start with, and it was found that the plethora of resonances discovered in bubble chamber and counter experiments had an amazing symmetry that could be organized according to the representations of SU(3) . As an example here is the baryon octet.

It immediately implied the existence of a substructure to the baryons , in a similar way to the (proton, neutron) SU(2) symmetry as a substructure of the nucleus :two independent vectors, SU(2), three independent vectors SU(3).

The Gell-Mann–Nishijima formula, developed by Murray Gell-Mann and Kazuhiko Nishijima, led to the Eightfold way classification, invented by Gell-Mann, with important independent contributions from Yuval Ne'eman, in 1961. The hadrons were organized into SU(3) representation multiplets, octets and decuplets, of roughly the same mass, due to the strong interactions; and smaller mass differences linked to the flavor quantum numbers, invisible to the strong interactions. The Gell-Mann–Okubo mass formula systematized the quantification of these small mass differences among members of a hadronic multiplet, controlled by the explicit symmetry breaking of SU(3).

The spin-3⁄2 Ω− baryon, a member of the ground-state decuplet, was a crucial prediction of that classification. After it was discovered in an experiment at Brookhaven National Laboratory, Gell-Mann received a Nobel prize in physics for his work on the Eightfold Way, in 1969.

You state

I'm going to assume a particle collider is involved,

Not a collider experiment. The Omega minus was discovered in a K-proton experiment, the K- from the Brookhaven accelerator .

It was the solid evidence of the consistency of the quark model, since it was discovered after its prediction as missing from the symmetry of the decuplet .

The first Omega- event in the Brookhaven bubble chamber

The theory developed further into SU(3)xSU(2)xU(1) with the strong interaction coming in strongly, and the charm, bottom and top resonances were discovered after the theoretical prediction, the charm with the j/Psi in the SLAC collider in 1974.

Then came the realization that even though QCD would not allow the quarks and gluons to be free, the signature of these particles would come in jets of ordinary protons, pions, kaons etc. as proposed in 1978 by J.Ellis et al.

At present colliders jets are considered the experimental signature of quarks and gluons in the search for new particles and resonances.

The quark model not only explained the plethora of new particles (baryons & mesons) discovered throughout the mid 1900's - it also predicted many new particles. Of course, the predictions developed as the theory developed. Those predictions made that were experimentally verified constitute great evidence. See this list of particle discoveries, particularly during and after the 1960's.

My answer is extremely brief, so I hope some more knowledgeable people can give better answers to this.