When i see a picture of the kingdom of Asturias in 790 i cant help but wonder how they drove back such a dominant force. Especially when i think about how small the christian kingdoms were in contrast to the muslim ones.
Note that this isn't an answer to the whole scope of your question, but only for a certain period of the whole Reconquista.
By 1009, Spain was divided between Al-Andalus and the christian Kingdoms (León, Pamplona, Aragón and the Coumty of Barcelona). The other half of Iberia was governed by the Caliphate of Cordoba, an independent muslim state. By 1009, the Caliph Hishan II was forced to abdicate. Afterwards, the Caliphate broke into a period of high inestability, with many small kingdoms claiming independence from the Caliphate, and creating the kingdom of Taifas. By 1031, the Caliphate of Cordoba disappeared, and the muslim part of Iberia wasn't unified, but divided in many small kingdoms who fought each other.
The christian kingdoms took advantadge of this situation, and pushed south to gain more land against the weakened mulsim kingdoms.
By the time that the muslim kingdoms had been reunified again, the christian kingdoms already had the upper hand in the Reconquista.
(I'm not an expert, and I may have missed/forgotten some key information).
