Let's say I'm running a workshop or a large farm and I need some slave labourers. Where would I go to obtain them? Were there slave trading businesses?
A big question is what period are you referring to? The slave situation is very different in the Republic when the empire was growing and slaves were flooding in from the constant wars. When you get to the Empire, the wars of conquest generally stop and so there's no cheap influx of slaves anymore. This brings you the question of where slaves came from in the Principate and there are generally two theories: one is slaves generating more slaves (the Self Replacement Hypothesis), the other is that there was a brisk slave trade from the periphery of the empire. We know Delos was a major slave market in the Empire and I've seen pretty convincing attacks against the SRH theory (but this isn't my specialty).
Also your location will matter as well. Slaves tended to be concentrated in the core (e.g. Italy) and were fewer in the provinces (say 10% of the population). So if you're located outside of Italy, you might depend more on free labour instead.