I'm not familiar with any sources that discuss pre-Islamic body hair practices, but as Muhammad, according to the hadith, mentioned "removing the pubes...[and] plucking the hair under the armpits" under a legal category called "fitrah" it's safe to assume that this was common practice. Fitrah refers to those hygienic actions that are so widespread and necessary as to be obligatory for non-Muslims as well.

As to how they did it, well, we already mentioned plucking as one option. Although the safety razor hadn't been invented, the pre-Islamic Arabs still had access to good old fashioned normal razors (i.e. very sharp blades.) They also had a chemical depilatory paste called "nura". Nura was a paste of either quicklime or quicklime mixed with arsenic.

Source wise: see any of the hadith on "fitrah" and the Encyclopaedia of Islam entry on Hair "Sha'r"