This is something I've thought about after seeing Episode III, but why is the rebellion slow to start up? The rebellion was effectually born in ROTS, you'd think in 19 years they would have been able to liberate a few outlying planets, or at least a portion of them.
I always believed there was no real reason for many to rebel until the Death Star came around.
If I recall in the Force Unleashed video game it is suggested that the Rebellion was actually formed by Vader's apprentice, which was part of a complicated plot by the Emperor to get those members of the senate that opposed him to expose themselves.
Other than that, little is known. Hopefully the new live action TV show will shed more light on the subject.
I believe it was mostly just the average person didn't care about the rebellion or think the Empire wouldn't bother them at least up until the Destruction of Alderaan showed most people that even if they submitted to the Empire's rule they might still be killed and had nothing to lose by rebelling. The Death Star's destruction also showed people that the rebellion might succeed in toppling Palpatine's rule.
Mon Mothma, Bail Organa and Garm Bel Iblis started the Rebellion early on but had a slow start at getting forces together (as Gaven Scott pointed out many worlds not important to the Empire were largely left alone and they didn't want to risk rebelling). It wasn't until that the Rebellion Leaders learned of the Death Star, did they really feel the urgency to act and steal the plans to learn to destroy it (as shown in ANH).
Also of note, Bail Organa probably realized that Luke and Leia were going to be the key to restoring the Republic and he probably wished to wait until they were old enough.
If I recalled in the Force Unleashed video game, Bail explains at this point they don't have the resources to engage the Empire.
I always thought the rebellion started a couple of years before A New Hope, and not the whole 19 years between ROTS and ANH.
The Rebellion was originally a political movement. It wasn't until it became clear that political means wouldn't bring back the Republic that they started resorting to attacks and guerrilla tactics. When they had enough means and support, it became open warfare.
Also in the books it is explained that two of the people who formed the Rebellion, Mon Mothma and Garm Bel Iblis had a disagreement on how best to oppose the Empire, which led to the forces splitting up and any sort of rebellion slowed down.