How was the onset of the Cambrian period dated?
Fossils are only in very rare cases dated directly, because they do not contain sufficient radioactive isotopes for dating.
Most geological periods are first and foremost defined by biostratigraphy- fossil assemblages, typically. 
The Cambrian period starts with the Fortunian stage - this stage is defined by the appearance of a certain trace fossil in Fortuna peninsula, eastern Canada, but is correlable with similar formations world wide. The whole discussion on how this stage is defined is available here.
As outlined in this paper, in addition to fossils, the Fortunian stage hosts various volcanic rocks which contain zircons, which can be dated by U-Pb. The age of the actual boundary is then interpolated from these data.