Having read some survey-level histories of the region in this period, I'm at a loss: On one hand, Magyar raiding parties are described as far-reaching and immensely successful on the battlefield, penetrating as far as northern Iberia and southern Italy. On the other, there are no mentions of attempts by the Magyars to occupy territory outside of the Carpathian Basin; I also don't have any idea as to what affect these campaigns had on the demographics, economics, or politics of raided regions, particularly those such as central Germany that were passed through frequently.
Basically, I'd like to better understand how these campaigns were provisioned and directed, what their typical targets were, what they devastated, and what they left untouched. What were their immediate and long-term consequences? How was it that they did not result in permanent conquests while still managing to be so long-range and widespread? Do I have a mistaken idea as to their actual scale?
In my experience English-language sources tend to focus on these being fearsome raids, while Hungarian language sources tend to focus on them being mercenaries hired by various Western powers fighting each other, such as Arnulth of Carinthia and Berengar I fighting for the throne of Italy, Hungarian sources mention being once hired by Arnulth and twice or three times by Berengar. Looting the countryside would be part of the job, to deny the enemy resources, although of course it was lucrative, too.
There were plenty of actual raids as well, they were timed to times of turmoil like when a king has died and the heir not yet fully in control, appearing quickly, looting, disappearing before defense is organized. The whole thing depended strongly on scouting, to find the right time when looting can be done without much resistance. To conquer, and especially to pacify and keep a region is entirely different.
They liked to loot monasteries (such as around Reims), and of course monasteries would produce and keep written chronicles, and this may suggest at overestimating its scale. It is a different thing to scare monks or to scare knights.
There were plenty of failures and defeats before Lechfeld. 838 the raid on Saxony was a failure, and never tried Saxony again. In 940 Hugo I, King of Italy would hire them against Alberic who held Rome and the region around it, that was a failure too.
That part of getting as far as Spain... In 942 Hugo sent them to take Cordoba, for whatever reason, or suggested to loot Cordoba because it is rich or something, my sources just say he directed them to Cordoba because they did not want them to loot Italy again.. Never reached Cordoba. Most of the wars were focused on Germany/Italy/Byzantine, the neighbors.
Instead of scale I would focus on frequency and speed, basically there was some campaign launched every year between 899 and 955. To me the impressive part is the amount of distance travelled, basically every year quickly getting somewhere far while avoiding enemy strongpoints, looting, getting back quickly. Totally speculative but I think something along the lines of not travelling on well guarded war roads, but just through terrain? The whole thing made possible by scouting, and by it being a fairly chaotic period, the more I try to look into what happened in Italy in the 10th century the more my head hurts.
Of the English sources Spinei, Victor (2003). "The Great Migrations in the East and South East of Europe from the Ninth to the Thirteenth Century" is most useful, Hungarian historians work from that too.
Tom Holland's Millennium covers Magyar incursions, basically in his reading the raids fed into the general sense of millennialism that was simmering in western Christendom in the run up to the 1000's. Basically, according to Holland, as previously unknown heathen raiders erupting from the east they would be comparable (if you were a Early Medieval educated Christian) to the biblical "Gog and Magog" as harbingers of the end times. When the Magyars were finally brought to heel at Lechfeld it was a major boon for Christendom and the legitimacy of the German king Otto the First.
Now if you consider the fact that the Magyars were largely a light-cavalry force facing European forces mostly comprised of light to heavy infantry it's fairly easy to see why they were so successful. Being lightly equipped and mobile would have made relatively easy for the Magyars to live off the land while on campaign, while their sheer speed would have allowed them to avoid any serious opposition or out-flank and envelope the enemy when forced into a pitch battle.