I can't say for the entirety of Europe, but I can give Eastern perspective, specifically - Russian.

First time Russian principalities heard of the firearms happened somewhere in the latter half of the 14th century: we can't say for sure as the exact date is disputed. There is an instance of Russian forces capturing some primitive cannons from Bulgars as early as 1376 and it is quite possible they were used during the siege of Moscow six years later according to at least one source (though some historians argue they were actually bought from the West). Ipat' Chronicle has a small note written in 1378: "Foreigners from Venice [recently] invented fire shooting", clearly referring to the first firearms.

Russian armies seemingly quickly appreciated this new type of weapon as it is known that by 1400 there already were small powder making factories in several cities, including Moscow, Novgorod and Tula. Such quick adoption of the powder weaponry can only be justified by it's usefulness, so even if it's quantities were small and quality left a lot to be desired, it still showed formiddable performance on the field of battle. It is worth noting that firearms technologies were somewhat lagging beind the West since Russians rarely used firearms and cannons in the open in large quantities, preferring to operate them from or against city walls. It is not known of any large arquebus-wielding troops during this period although many different types of handcannons and cannons were used by many garrisons: for example, Vologod-Perm Chronicle (describing battle of Galich) states: "... And the fire from the city walls was opened with many small and big cannons, pischals (= arquebus) and samostrels (literally "the thing that shoots itself", referring to different types of small arms)". There were no complex tactics and its usage by Russian principalities outside of cities often amounted to including some random gunner squads with soldiers often employing mixed types of small arms to scare off enemy cavalry or to deal with heavily armoured foes.

The change from the old form of warfare was not imminent and most likely took many decades to completely change the way conflicts were fought. It many descriptions of field battles (Shelon, Cheloha river, Suzdal) in 15th century firearms are not mentioned at all. The first truly decisive use of small firearms and cannons most likely happened during The Great Stand at Ugra River, where many firearms wielding infantrymen prevented Tatar host from crossing the river and forced it to eventually concede defeat and retreat. From then on firearms begin to play major role and constantly evolve with Ivan IV The Terrible forming first professional Russian arquebusier corps in the form of Streltsy ("Sharpshooters").