Now that is an interesting area that I don't know about - How did Edison generate his DC? Did he generate AC and then rectify it into DC? That would be very inefficient.
I would think that his generator would be in the form of a dynamo (as opposed to an alternator). A dynamo makes use of a commutator (just like a dc motor) to switch the direction of current so that it doesn't alternate.
Dynamos were commonly used in cars for battery-charging purposes, until they eventually got replaced by alternators (this change being made possible by the advent of cheap solid-state rectifiers).