Do you mean historically at first ?
Or do you want a list of all the checks that have been performed since ?
Or of all those that we know could be performed in principle ?
In principle one can perform so called deep inelastic scattering of leptons (electrons, muons and neutrinos) on protons and neutrons. Then one can measure how theoretical structure functions compares with experimentally obtained ones. This is since the charge leptons will couple to the quarks mainly by the EM-interaction, wheras the neutrinos only coulpe via the weak interaction. Then one will an expression that contains the sum of the squared charges of the u and d quarks. This can be then tested against experiemt.
There is a quite nice description of this in the book by martin and shaw, called 'particle physics", chapter 7. A nice and cheap book that guides one through the history of particle physics :-)
So how do you measure that it have 3 u-quarks then? ;) It is a resonance so you must deduce its quark content from its decay products (proton + positive pion). And that only leaves you with theoretical considerations, not pure experimental data.
How can you from pure experimental data deduce that the delta++ resonance had 3u quarks? It is similar to say "A omega minus baryon has 3s quarks and charge 1 minus, hence a s-quark must have the charge -1/3).
Historically, one first observed a whole bunch of hadrons, of different masses and charges. In order to describe their properties, one postulated a kind of quark model, and from symmetry reasons, one predicted several other hadrons to exists, and they where found. However, it was not until the birth of deep inelastic scattering of protons and neutrons one could really measure the valance quarks charges.
That was how one determined the charges of the quarks experimentally.
You don't think a lot of theoretical analysis goes into DIS, which only looks at sums of parton charges squared anyway?
DIS does require a lot of analysis to extract all the distributions together from global fits of all available observables.
Besides, the ongoing work on the quark structure of hadrons does not end to DIS and the optical theorem. Deep exclusive processes provide much more information theoretically /experimentally, such as (for instance) the energy momentum tensor of the partons. If you wanted to extract the energy momentum from DIS-like applications of the optical theorem, you would need to scatter gravitons.
So, we do know a lot about partons in the hadrons, this does require a lot of analysis, some of which has not even be put into code yet (not to mention performed).
