I think the typical hierarchical resistance military force seen as the Rebel Alliance was still a fairly new entity by Episode IV. The years after the Clone Wars would have seen the Emperor as the victor and the guy that restored peace to the galaxy. There wouldn't have been any popular resistance at all to his rule. He brought peace, he controlled the money as we've now seen in TCWs. There were the very select few who knew who he was but they also knew they had no way to prove it and no chance of standing against him militarily or politically.
The years following the end of the Clone Wars I think Bail Organa and those select few probably spent the bulk of their time gathering evidence to show what the Emperor was to be used to convince others, and probably assisted in a kind Jedi underground railroad, to spirit and hide away as many as they could. They probably then turned their efforts to goading the Emperor into actions that would foment dissatisfaction with his rule. That could then be grown into more open resistance.
There were probably deals made with organized crime by both sides, which is essentially the ready made covert non governmental organization that exists in every society.
Hubris on the Emperor's part led to him caring less and less about the subtleties of politics as time went by, which eventually led to openly enslaving worlds and ultimately more open resistance. Probably by that point Organa and the original cadre of folks from the early days began their moves at forming a more active resistance.