For the byzantines -- armies who had vastly more organization and discipline than their european counterparts in the 10th century or so -- the tricks were basically discipline combined with foot archers. One particular fact to keep in mind is that the bows horse archers used were shorter, had shorter range and very limited power and accuracy compared to foot archers.

So, Byzantine discipline would keep the infantry formed and lines of spearmen in front of the foot archers. The foot archers would hold their safe ground and use their superior range and hitting power to discourage the horse archers.

Source: Sowing Of Dragon's Teeth, a collection of Byzantine Military Treatises' from the 10th century.

The Hungarians were badly defeated during the first (1241) Mongol invasion of Hungary, and the Mongols occupied the Hungarian Plain. They withdrew due to internal Mongol politics. A second invasion came about 1285 and a third thereafter.

These last two invasions caused heavy Mongol casualties, partly because the Hungarians had built many fortified strong points that provided a defense in depth. This allowed weaponry such as the crossbow to be used effectively, and there was less emphasis on meeting the nomads in open battle.

Certain states in the Middle Ages, such as Kiev, beat nomads such as the Polovtsy many times. A lot of this success had to do with discipline plus professional soldiers who were familiar with nomad tactics. The Mongols for a while did well with Turkic soldiers led by Mongol officers, but eventually the settled societies adapted to any Mongol innovations.

Mobility allowed the nomads to stay dominant on open, grassland areas, until firearms became used in large numbers by settled societies. The nomads could not match settled cultures in either manufacture of these or numerical manpower.

Rene Grousset in EMPIRE OF THE STEPPES makes mention of firearms and artillery used by the Russians. Muhammad Girei was halted by Russian artillery in 1523, and in 1581 the Russians conquered into the Khanate of Siber, using muskets. The 16th Century was the time when firearms became an important factor, increasing with every passing decade. The nomad economies in general had not enough wealth and not enough talent to compete in the manufacture of these.

Sometimes it was just by having good armor and shields. Because of horse archery being a classic trait of the Turkic people, Saladin had access and use of horse archers during the Crusades. The main tactic he used with them was to basically harass the enemy until they broke formation and charged. Superior armor and shields meant that this wasn't a significant way of killing off your enemy, but a smart tactic to get an undisciplined force of charging forward and creating openings for you to massacre them.

A good example of this is the Battle of Arsuf, where Saladin tried to use archers and horse archers to harass Richard the Lionheart's men into breaking formation. It failed because of their superior discipline. A noteworthy fact was that the archers did not have the effect of killing large numbers of their enemies, but rather were to harass them until they were annoyed enough to charge against their general's orders.