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RE: What does an experimental particle physicist do: Measure particles!
The top quark is special in the sense that it decays into a bottom quark and a W-boson very promptly, so that it has no time to do anything else. We can reconstruct it from the measurement of the properties of the decay products that can be somehow identified.
For the light quark stuff, please check my answer below and this link.
Does it help?
Now I see what you meant by reconstruction from decay products... I will still dig into the fermions and bosons... I only know a little bit about them.
If you want, you can have a look to my last posts where I started to write particle physics lecture notes for steemit. This is a kind of starter (see here for the lecture number 1 which may answer your fermionic/bosonic question).