The short answer- they didn't. Then, as now, the steppes were lightly populated compared to the more fertile and developed areas around them. In 1206, when Temujin united the Mongolic peoples into a single nation and took the title Genghis Khan, there would have been probably a couple million people under his rule- compare this with the contemporary Song dynasty in southern China, with perhaps a hundred and twenty million.

Now, the much more interesting question is, how did this relative handful of steppe people create such an enormous empire? There are several answers, but the most salient is that they leveraged their population to an enormous extent, far more so than the settled civilizations they fought against.

In an agricultural civilization, because the vast majority of people must be engaged in farming, military forces are correspondingly small. You can either take the Chinese (and modern) route of having a standing army answerable to and supplied by the head of state, representing a few percent of the population, or the European model of calling up relatively wealthy individuals who could provide their own arms (also a small percentage), both of which could be supplemented by peasant levies when necessary. For the Mongols, essentially every able-bodied male was a fighter. They had no need to return home and work their fields, because their food (and their homes) moved with them. Horses were a necessary part of everyday life- the Mongol word for 'poor' derives from the verb 'to walk on foot', to give you an idea of the centrality of horses to their lifestyle. Constant inter-tribal warfare meant that every man was trained with the bow.

So, while the settled peoples they fought against could raise armies representing a few percent of their population, the Mongols could bring to the fight essentially their entire male population, each of whom would be an excellent horseman and fighter. This wasn't enough for anywhere near parity, of course, but it brought the odds down to the point where victory was feasible. The rest - the reason they could defeat armies five or ten times their size - has to do with the prowess of individual Mongols, their innovative tactics, strategies, and organization, and their willingness to adopt new methods of warfare (and huge numbers of auxiliary troops) from those they conquered. Without the demographics being in their favor, however, none of that would have been enough.

The Huns had been in Europe for years, so they were not really conquering from Central Asia even though they had their origins there. The reason for their numbers was mainly that they incorporated the migrating Germanic tribes into their confederation.

This became an issue at the Battle of the Catalaunian Plains, the Romans allied with some of the Germanic tribes (Visigoths, Franks, Burgundians, Saxons, etc.) against the Huns. After the death of Attila, many of the tribes (Gepids, Ostrogoths, Heruli, Rugii, Suebi, etc., who had been on the Hun side of the Catalaunian Plains) rebelled, breaking up the Hunnic horde.

There were also non-Germanic tribes involved like the Alans.

The areas weren't densely populated back then either, they had large armies because everyone in their society was a warrior. The harsh steppe climate kept generating fierce peoples where one group would become dominant, become too large to sustain itself, then proceed to wreak havoc an their agricultural based neighbors. Scandinavia had a similar effect and was called the womb of nations.

Keep in mind that the Mongol empire was the single largest contiguous empire in history. It's not just that they were great fighters or that a large percentage of their population took arms. When they would move into foreign countries, they would absorb the locals into their armies, with the Mongol core leading. Eventually, as they got deeper into Europe, Europeans in Hungary or Poland may have found themselves fighting against Russians who were absorbed into the Mongol army (under threat of death). In other words: They were like the Borg. Absorb or die. This turned into a very effective route towards growing their empire to a continent-spanning size. Something that would have been impossible were it just Mongols, due to their small numbers.