In being very scarcely funded before the war, the Finnish air force had a blessing in disguise as a curse. The shortage of planes meant that they could have near-superhuman requirements to become a fighter pilot. Only the best of the best of the best in Finland would ever become fighter pilots.
Finnish fighter pilot training was also extensive, very hard and focused a lot on shooting. Jorma Sarvanto, of shooting down 6 Russian bombers in one mssion with his Fokker D.XXI during the Winter War fame notes that immediately before the Winter War, during the 24. Fighter Squadron's training at Kexholm and over Lake Ladoga, he conducted no less than 18 live fire exercises during 14 days in July 1939 in order to become a good enough shot to pass his fighter pilot training.
The Finnish air force was also first in the world in using the more modern rotten-schwarm (or fighting pair-finger four) formation rather than the older v or vic formation. The Finns experimented with this formation from 1932 and fully adapted it in 1935. The older formation consisted of a tight formation of 3 planes in a V formation with the centre plane a but further ahead and the flanking planes on either side slightly behind. However, the vic formation was based on ww1 tactics, when radios had not been common equipment in planes and communications and order-giving relied on the subordinates being able to see their flight leader. Thus the formation was tight, so that the flight leader could communicate with hand gestures or by "wiggling" the wings of his plane.
The rotten-schwarm tactic relied on two planes further apart, and with another pair even further away and above them. The flight leader could communicate by radio and did not need to see his wingman. The formation was larger and thus covered more space, making it easier to spot enemy formations and harder to for the enemy to spot your own formation. The wingman was also in a prime position to attack any plane that tried to get behind the flight leader's plane and the two planes above and behind in a good position to attack any planes trying to get behind the wingman.
The Germans developed the same tactics during the latter part of the Spanish Civil War and used them to great effect during the Battle of France, casuing the RAF to switch to the German tactics during the early parts of the Battle of Britain.
The Finns also developed their own version of boom'n'zoom tactics. The US Army Air Force developed this tactic over the Pacific during the later part of ww2, refusing to get into dogfights (or "hairballs") with the nimble Japanese Zero fighters and instead opting to climb high, dive on the Japanese planes from above and use their heavy armament to shoot down Japanese planes and then their superior engine power and speed to climb again, where the Japanese fighters with their less powerful engines could not follow, to rinse and repeat.
Since the Finns lacked the powerful engines of late war US fighters, their version instead relied on skilled pilots that knew their planes intimately. The Finns would climb as high as they could, and when they spotted a Soviet formation, they would dive on it. Excellent shooting skills extensively trained would let them destroy or damage one or several Soviet planes. The Finns would then continue to dive through the Soviet formation, often drawing the Soviet fighter escort after them, leaving the other Finnish planes to attack the unescorted bombers, or dive after the Soviet fighters.
The diving Finnish plane would then continue to dive to tree-top level. Only a skilled pilot that knows his plane inside out knows how far he can dive before he needs to pull up to fly at tree top level after a long high-speed dive. The Soviet pilots, often less skilled and not experienced in these tactics would either pull up too early, at which they most often lost the Finnish fighter against the forest on the ground due to focusing on pulling up and not crashing or would simply pull up too late and crash. The Finn would then continue at tree top level until he had shaken any Soviet pursuers off, and then climb to repeat the process.
But extremely skilled and well-trained pilots with modern tactics was not the only thing that made the Finnish Buffaloes successful. The Finns received B-239 Buffaloes, that had the more powerful 980Hp engine (rather than the 950Hp engine the other Buffaloes had). The Finns also equipped their Buffaloes with lisence produced versions of the excellent German reflector sights, which was a strong improvement over the telescopic or ring sights most other Buffaloes used.
The Finns also de-navalised their Buffaloes, removing the tail hook and the emergency raft, which saved quite a bit of weight. The Finnish Buffaloes were also delivered without armour, but equipped with a back rest armour in Finland, giving the pilot decent protection at a smaller drawback of extra weight.
The biggest improvement of the Finnish Buffaloes were their armament - the Buffaloes used by the US were about half equipped with one .30 MG and one .50 MG and half with one ,30 MG and three .50 MGs. The Finnns armed theirs with four 12,7mm (.50) FN-Browning machine guns. These had a significantly increased rate of fire (~1 100 shots per minute) compared to the US AN/M2 (~850 shots per minute).
So, the bottom line is that the Finns had better Buffaloes through reduced weight, a slightly stronger engine, armour (the earlier versions of the US Buffalo lacked armour), much better armament and a much better sight.
The Finnish pilots were superbly trained and many of them veterans of the Winter War, had very high shooting skills and used locally developed modern tactics.