We are talking about a process that spanned over 780 years from the Arab conquest of the peninsula in 711 to the fall of the last Muslim statelet, Granada, in 1492. Things were far from uniform over those centuries, to put it mildly - see [this discussion] (https://www.reddit.com/r/AskHistorians/comments/4ovuao/la_reconquista_was_reconquest_a_term_used_at_the/) we had recently, for example.

The first three centuries saw very little reconquest as the Christian polities in the peninsula were too insignificant to do anything against the united Muslim south, Al Andalus, a sophisticated urban civilisation and arguably the most powerful state in Europe of that time. It was only after the Caliphate fell apart in 1031 that the Christian states could start conquering in earnest. At this point there were several Muslim states (the so-called taifa kingdoms) and several Christian kingdoms or counties. These would at times ally across the religion divide but overall the Christians would slowly gain an upper hand, most notably Castile that conquered Toledo, the ancient capital of Visigoth Spain, in 1085. Eventually Muslims grew alarmed enough to invite the Almoravids, a Berber sect-turned-into-an-empire, over from Marocco even though they had reasons to suspects those Berbers would take over their Iberian kingdoms. As the emir of Seville allegedly remarked, 'I would rather herd camels [for the Almohads] than swine [for the Iberian Christian kings]'. These guys managed to stem the Christian advance but they could not stop or reverse it - nor did the Almohads, the even more fanatical Berber dynasty that replaced them in the 1140s.

The various Christian kingdoms were far from united in their push against the Moors. But they did join forces at several occasions (with some major prodding from the Papacy and monastic orders). Most notably, in 1212 the joint forces of Castile, Aragon, Navarre and Portugal crushed the Almohads at Las Navas de Tolosa. This was the one most important battle of what we now call the Reconquista. Once the Almohads were defeated the Christian kingdoms of Castile and Aragon swiftly conquered most of the rest of the peninsula over the following decades. These were not joint campaigns but they were sort of coordinated (and the future land gains were divided beforehand by treaties). By the late 1200s the Reconquest was all but complete - save for a few holdout strongholds along the southern coast and the rump emirate of Granada that was allowed to go on as a vassal of Castile until they took it over in 1492.

(Sorry for a brief reply. I've got to go now, will be back tomorrow. If you have any more questions, fire away).