The Visigoths as a group emerged in the wake of the Battle of Adrianople in 378 as a composite of various Gothic peoples, including the Teruingi, the Greuthungi, and other ethnic groups from both sides of the Danube River. By the late 4th century, this confederation was in the military service of the Empire, though needless to say, the relationship could be rocky (see the Sack of Rome in 410). The Visigoths under their king Wallia (415-419) were sent to Hispania to combat the Vandals, Sueves, and Alans who had invaded the Iberian Peninsula in 409. The Visigoths saw some measure of success, but a new treaty in 419 resulted in a resettlement of the Visigoths in Aquitaine to subdue the Bagaudae, a group that was wreaking havoc in the Gallic provinces. Southern France, in particular the Narbonne region centered on Toulouse, would be the base for the increasingly autonomous Visigothic kingdom for the better part of the next century.

Meanwhile, the Sueves and Vandals were continuing to press their advantage in the Iberian peninsula. The Sueves had more or less been confined to the province of Gallaecia by the Vandals, but following the latter's departure for Africa in the 440s, the Sueves embarked on a series of rapid conquests and managed to incorporate Lusitania and parts of Baetica into their growing kingdom. (map). Though a treaty between the Empire and the Sueves had halted their progress temporarily, the death of Valentinian III saw the termination of the agreement and the reopening of hostilities. The new emperor Avitus declared war and in 455/56 the Visigoths, again operating as Rome's allies, provided the troops. Under the leadership of Theoderic II (453-456), they crushed the Sueve troops near the city of Astorga, seized several key centers of Sueve power such as Mérida and Braga, and executed the Sueve king. The operation and ensuing succession crisis effectively stunted the growth of the nascent Sueve kingdom and paved the way for Visigoth hegemony in Iberian political affairs.

In spite of this, the Visigoths retreated back into France following news of the death of Avitus. In the following years there does not appear to be much evidence for any permanent Visigothic settlements south of the Pyrenees, though it is possible that military garrisons controlled small pockets of territory in Carthaginensis. For all intents and purposes, however, the region was under the de facto military authority of the Visigoths. Ricimer and his puppet emperor Libius Severus increasingly left military affairs in the hands of the Visigoths, as the imperial government lacked the ability to impose their authority on lands outside of Italy.Theoderic II continued to intervene in Iberian affairs, at times independent of Roman authority or counsel.

The next important phase of expansion took place during the reign of Euric (466-484). In 469 war broke out between the Visigoths and the Empire over a dispute in the Gallic provinces, and Euric took the opportunity to expand the borders of his kingdom. In the summer of 472, Visigoth armies conquered Tarraconensis and it is also possible that during this time Visigoth troops occupied the interior regions of Carthaginensis, connecting the pockets they had controlled since the 450s. When Julius Nepos came to power in 473, he quickly negotiated a new treaty with Euric, recognizing the king's sovereignty over his territories in Gaul and Hispania, though Visigoth troops were still to be at the disposal of the Empire.

Visigoth settlement in the peninsula really does not appear to begin in earnest until the late 490s/early 500s, though the matter is certainly up for debate. As others have pointed out, the Visigoths were always a minority group; Roger Collins estimates no more than 30,000 persons during the period 392 to 419, and the more extreme estimates for the same time frame number only 100,000. The groups that entered Spain would not have been drastically larger. Their impact on the genetic makeup of Hispania would have been minimal.

Resettlement was likely fueled by increased pressure from the growing Frankish kingdom to the north, which in 507/508 would overrun the Visigoths' Gallic territories, bringing the kingdom in Toulouse to an abrupt end. Though the Visigoths managed to regroup at Narbonne, the city was conquered by the Ostrogoths the following year, ushering in a brief period of Ostrogoth dominion over the Visigoths during the reign of Theoderic the Great. Following his death in 526, the Visigoth monarchy was able to reassert its sovereignty and from the 530s on, was increasingly focused on its territories in Hispania, with Toledo emerging as the center for the revitalized kingdom. Over the next century, the Visigoths would slowly consolidate their power in the peninsula, annexing the Sueve Kingdom in the 580s and subjugating (sort of) the Basque Country. The Byzantines on the southern coasts would not be expelled until the seventh century, and maintained a toe hold on the peninsula for quite a while.

The process of creating an independent Visigoth kingdom in the Iberian Peninsula was a gradual one. As in other parts of the Roman world, early 'barbarian' authority derived from their status as imperial enforcers in territories the emperor could no longer effectively administrate. Imperial control over these groups was always tenuous at best, and over the course of the fifth century, groups like the Visigoths increasingly assumed de facto control, even if they ruled in the name of an emperor. Gradually the Visigoths shed their imperial obligations, though the accoutrements of imperial power and authority would linger for quite a while, just as it did in the rest of the Roman world (arguably it still does in some respects).

As far as place to get started reading, if you have access to the Cambridge Histories online edition, there are some great introductory texts to the formation of the Visigothic kingdom and the time period in general. Roger Collins' book, Visigothic Spain 409-711 provides a good overview of the kingdom's history. Enjoy!

The Visigoths were one of the many germanic groups roaming the territory of the decaying west roman Empire in the 5th century. They worked as a kind of mercenaries and were granted the right to settle in what is know southern france. Later, the central authority of Rome deteriotated even further, and the Visigoths were put under pressure by other germanic people - the Franks - from the north. They used the power vacuum in the south to expand into what is now Spain.

It should also be noted that the Visigoths are only a part of the ancestors of modern day Spain. They lands they conquered where settled by romanised descendants of iberic celts, and whoever migrated there during the roman empire. Also, in later times a lot of north african people migrated to Spain.

There is a ton of literature about the fall of the western roman empire. A relatively recent book I enjoyed - and which covers the Visigoths in quite some detail - is "The Fall of the Roman Empire: A New History of Rome and the Barbarians" by Peter Heather.

One series you should seriously consider reading is the trilogy of books about late antiquity by Peter Heather. They are popular enough that getting hard copies of them should be relatively trivial, although I also know ebooks of them are available as well. I recommend Empires and Barbarians: The Fall of Rome and the Birth of Europe as it talks about what you are interested in in particular.

One thing I should note; the Visigoths in Hispania are not strictly speaking the core of the 'Spanish' peoples. The Germans made up a relatively small percentage of all the places in the Roman Empire they carved kingdoms out of, and the bulk of the population were Romanized peoples. Over time, these Germans were absorbed into the larger culture, as happened in Gaul and Italy. Pretty much the only place where Germanic peoples completely pushed out the local cultures was in Britain, and England in specific. Ironically, this is also a good place to consider as a more modern example of how this might have played out, as the Norman kings and Lords of England became 'English' over time, the same as the Franks and Visigoths acclimated to the local culture.

As for a more direct answer to your question, how did that come to pass? Well, the Visigoths in particular were invited by the Romans in the 5th century to settle in Southern Gaul (modern France) like many other German tribes such as the Burgundii and Franks. They were granted nominal tax control over this area in exchange for fighting in the Roman Army. As Roman control broke down further, this went from a very regulated vassal relationship to more of an independent state within the nominal control of the Empire. So they were very close to Hispania. They crossed over there in the wake of another Germanic tribe, the Vandals, rampaging around and basically replaced an absence of Roman authority in the peninsula with their own.