We know so little about how the rebellion to restore the republic began particularly from the movies. There are though a few hints from the films and some from the EU that shed some light on to these dark times between the films.

The road to rebellion began with the end of the clone Wars and the declaration by Palpatine that he was reorganizing the Republic into an Empire. At the end of ROTS we see the leaders of the Trade Federation, Corporate Alliance, Techno Union, Intergalactic Banking Clan, and the Commerce Guild all killed and their droids deactivated. What we do not see are the individual worlds that left to join the Separatists being eliminated. We know that thousands of worlds left when they heard the call by Dooku to leave a corrupt and dieng Republic. What of these worlds that left on ideological differences with the Republic those who saw the Republic as corrupt would they return so easily to the Republic now that it was an Empire? I doubt it very much. It is clear that many embers still glowed from these planets long after the fire of the Clone War had died down. Perhaps continued skirmishes continued during this 19 year period. This would no doubt be why the Clone Wars is plural. These resistance movements would be separated from each other by the vastness of space. With no planets able to help one another the Emperor can invade or just raid these systems as he chooses.

Even though Palpatine made himself Emperor at the end of ROTS he still had to contend with the senate. This shows that perhaps the Emperor was not in full control of the galaxy. He might have held sway over most of the senate but he still had to keep them happy in order to maintain power. Chief Bast's line of, "Holding her is dangerous. If word of this gets out, it could generate sympathy for the Rebellion in the senate." indicated that senate still held some power in the Empire at this time. This is further confirmed when a few lines later Vader orders steps to keep Leia's capture a secret. Why placate the senate if it didn't have any power? It wasn't until the Death Star was operational that the Emperor was confident enough to eliminate the senate and really control the Empire.

The senate did have power and already did have some rebel sympathies. The founders of the Rebellion, Mon Mothma, Bail Organa, and then later Leia were members of the Imperial senate. Leia herself would use diplomatic immunity to go around on "mercy missions" to besieged worlds like Ralltiir and Toprawa to give support and to shuttle information though the lines. The leaders of the Rebellion could meet and organize in relative peace right under the nose of the Emperor. It would appear this interim period between the movies was a race between Palpatine and Mon Monthma. Palpatine races to build and implement the organizations and structures for a lasting Empire while Mon Mothma raced to build support to oppose the New Order.

Now the Rebellion really begins to take shape. The scattered embers from the clone wars are still fighting the empire. Despite these planets not having return to the rule of Coruscant after the war the Emperor would still hold claim to rule these worlds and thus declare them rebellious. This would be the excuse to have the senate pay for high military expenditures and ruthless police powers. Their plight has some sympathy in the senate from senators who would like to see these world brought back into the fold peacefully or left alone. These senators would also be most likely the ones opposed to the Emperors new powers. Mon Mothma being the most vocal of these senators is branded a traitor and has to flee for her life. While in hiding like Dooku she goes around the galaxy gaining support and preaching the ideals of the Old Republic. Since she is probably talking to a lot of former separatist worlds she is most likely referring to the ideals and structure of the founding of the republic 1000 years prior before the corruption. With the help of her friends in the senate she is able to move about and gain a lot of political support while uniting a lot of the already established resistance groups into one concentrated effort against Palpatine and to bring back the Republic. This culminates into the Corellian Treaty and a formal out loud declaration of a rebellion to oppose the Empire two years prior to Yavin.

An army and especially a navy needs to be formed. The local security forces or militaries of the rebellious planets would make an excellent backbone. They would have had to have fled their home worlds to find hiding in the galactic wilderness of the outer rim. The empire would be sure to crush any force that declared itself in league with Mon Mothma. Recruits would need a place to go to be organized and trained to fight. Criminals like smugglers and pirates might even join giving the Rebels an advantage in secret routes and hiding spots. Refugees from Imperial occupied worlds would need new homes. From these camps would come soldiers even if it was just a means to be fed. With the main force in hiding the rebels can train equip and grow a professional military to beat back the Empire. Resistance movement hardly ever gained its goals by guerilla tactics alone. Regular forces and meeting the enemy toe to toe has been the way to achieve victory in many rebellions. The Alliance military advisors and professionals would know this and would be what they were doing on Dantooine, Yavin, Hoth , etc... They were building a core fighting force that would be able to take and hold planets from the Empire while also giving tactical and logistical aide to the various resistance cells across the galaxy.

The Rebels seem to have been smart with their fleet. We can see in the missions from the game X-Wing how the rebels operated the fleet. The beginning of the game starts with a cut scene of the Battle of Turkana. In this scene we see a lot of Mon Cal cruisers and other assorted rebel ships being ambushed by a large Imperial fleet. The rebel fleet escapes but that battle must have been very frightening for the rebels. That was most likely the entire rebel fleet and it was almost destroyed. As the game goes on we see the player being transfer from a lone hidden frigate for training then a loan hidden Cruiser for missions. This shows that the Rebels keep their fleet dispersed. Probably having a large Mon Cal Cruiser in important sectors with its support craft scattered nearby to avoid detection and to avoid all of the fleet being caught at the same time. With use of hyperspace capable fighter craft they can strike Imperial fleets without exposing any major capital ship. The fleet can form by sector or the entire fleet as needed for larger actions then disperses.

Much of the early Rebellion would be attacks on Imperial convoys using hit a run. There would be raids on lightly garrisoned worlds and a lot of evacuations in the face of overwhelming forces. But eventually this rag tag bunch would become veterans and then well equipped veteran until they could begin to stand and hold ground against the stormtroopers. When they can do that they could begin to attack Imperial held worlds and begin to win freedom for the galaxy. They probably began to become this proficient around the time of Endor. After the death of the Emperor and Vader the Rebels were ready to mop up the fragmenting empire.