Quoting an earlier answer on German kill counts here, but followup questions are always encouraged!
It is also worth pointing out that while the Germans did have roughly 2500 aces, the Soviets had more at roughly 3000 and the US had nearly 1300 despite its late entry into the war. If you look at the list of top scoring aces the list is dominated by German pilots. You have to scroll down a long way to get to Richard Bong, the first American listed. Most of the factors that allowed these high kill counts for the top aces translate to creating aces in general.
There were several factors that contributed to the astronomical kill counts accumulated by German fighter pilots. The most important in my opinion is that they stayed in combat from whenever it was that they started until they were killed or incapacitated. The US and Commonwealth fighter forces were far more likely to rotate pilots out of combat into other roles such as training. For Hartmann in particular, that meant combat from 1942 to the end of the war with few breaks.
A second contributing factor was the excellence of German fighters. The Bf 109 was a very good fighter (especially early in the war), and the Germans were able to deploy it in combat in the Spanish Civil War via the Condor Legion. This allowed them to have combat experience that could be passed down to younger German pilots. This actual experience cannot be discounted. Even little things like learning what is likely to malfunction during combat is vital. This is especially true for learning what is important and what can be ignored in combat. Every model of plane is going to have its eccentricities, and knowing what you can safely ignore and what you must address immediately can be a lifesaver.
Another major factor in the large kill counts for German pilots is that they faced some seriously obsolescent aircraft on the eastern front. At the beginning of the war, their opposition had few fighters that could match the 109, and many aircraft that were hopelessly outclassed. The Russians also employed P-39 Airacobras among other aircraft supplied by the US, many of which were not a match for Hartmann's aircraft. Having a technological edge is huge in aerial combat.
The last factor I will mention is that the German aces were highly skilled. While it would be difficult to measure Hartmann's skill against an Allied ace, that he was an excellent combat pilot is beyond debate.
Lastly, there is some controversy over the claimed kill numbers. Some do not think that the German claims are accurate, and assert that the actual numbers are less than a third of the claimed counts. So far, I have not seen compelling evidence from these doubters, but that does not mean they can be completely dismissed.
/u/Domini_Canes has put the Skewed kill counts of the Luftwaffe into excellent perspective in answering this question, but I just want to add an addendum concerning Wehrmacht "Panzer Aces" and the apparent plethora of them compared to the paucity of them for the Allies.
The short answer is: The Western Allies in particular simply did not track it. We have two recorded "Tank Aces"; Lafayette Pool, a member of the US 3rd Armored, and Sydney Walters, a Canadian Armoured Corps member. The latter's kill count is listed in most sources as 18 enemy tanks. By contrast, Pool is listed as having destroyed "over 200" vehicles; of various classes, and you have to dig deep to find the breakdown of them. Both numbers for both aces are small, and their kill counts are indistinct and confusing. I will posit this: Their kill counts are most likely higher, but their recorded kills are realistic given the circumstances they occurred in. Further more their kills are tallied in a relatively short space of time, Pool's basically being limited to the Normandy Campaign and Walters from his unit's (2nd Armored Brigade, an independent flag level formation) arrival in Normandy to the end of the war.
The entire concept of 'tank aces' is incredibly hard to swallow, and there's just a myriad number of problems with Wehrmacht tank kill counts. First is just plain old fog of war; its quite hard to keep track of what the hell is happening around you in an armored vehicle, and the entire idea that you can pinpoint who killed what in anything beyond small unit action requires a great suspension of disbelief; and this is avoiding the problems of returned-to-combat vehicles, what constitutes a 'kill' and confirming kills in retreat. Secondly is the idea that it was in Nazi Germany's greatest interest to cultivate a cult of aces; attempting to show their individual fighting man as skilled, professional and superior to their enemy's. We see their ideological enemy, the Soviets, adopt a similar mentality as well, with Beevor mentioning Sniper Aces and even "mortar aces" and other such skilled infantrymen being mentioned and glorified in much the same way as skilled Fighter pilots or Tank commanders would be. They therefore went out of their way to embed reporters with notable tankmen and do their best to drum up the idea and image of superiority and skill; they bothered to keep track. I'd say that by contrast that it simply wasn't something that the Western Allies cared to attempt to track, and while the Allies definitely had their share of Fighter aces like Dick Bong, 'wreckage counts' for armored engagements tend to be touted proudly in unit, not individual histories for the United States et al.
Thanks for all the answers
They didn't send their pilots home. American and Commonwealth pilots (can't speak for the Russians) had tours of duty, where they'd undergo a certain amount of missions before they were sent home to train other pilots. German pilots would fly missions until they were killed, injured, or captured, leading to individual pilots flying a ridiculous amount of missions and gaining experience, but not being able to pass this knowledge onto the recruits.
I just want to point out that the Luftwaffe was part of the Wehrmacht. The Wehrmacht was the Defence Force (yes, even the Nazis considered their military a defence force). It consisted of the Luftwaffe (Air Force), Heer (Army) and Kriegsmarine (Navy).
Hitler sent about 12K Luftwaffe volunteer personnel to support General Franco in the Spanish civil war, and gave them Stuka's and Messerschmitt's to play with.
http://www.century-of-flight.net/Aviation%20history/WW2/Spanish%20Civil%20War.htm
They had confirmed ace pilots before WWII started, and those pilots were training/leading the air war for Nazi Germany. They developed new bombing techniques and honed their experience in dogfights, even initiated the first mass troop airlift.
As a side note, for those interested, the Germans also had most of the top Panzer (tank) Aces of the war; as in, tank commanders with the most confrmed kills. The top 4 Tank aces are all German. Kurt Knispel, a Sudeten German, had at least 168 confirmed tank kills. The top Allied Ace was Dmitriy Lavrinenko, at 57 tanks.
One can drew numerous conclusions from this. Maybe the Germans just had very good tanks and were therefore harder to kill and better suited to kill? Yet the German tanks were very subpar until the arrival of the Tiger 1's and the Panthers in early 1942. Maybe the Russian/Allied tanks were bad and therefore easy to destroy for the Germans? Yet the Soviet tanks were very good, the K1, K2, and T-34 (and its variants) of the Soviets were all formidable tanks. Or maybe the Germans just had tank crews that were better trained and more skilled? This is probably the most sensible answer, even though the quality of (most newer) tank crews began to freefall as the war came to a close.