Why did so many separate countries declare Independence from Yugoslavia in such a short period of time? As an outsider it is hard to even figure out which modern countries are the decedents of Yugoslavia, (slovenia, serbia, croatia, bosina & h, ?)
Yugoslavia consisted of 6 republics (Slovenia, Croatia, Serbia, Bosnia and Hercegovina, Montenegro and Macedonia) and two autonomous regions (Vojvodina and Kosovo, both part of Serbian republic).
Causes of break up are numerous, and it would take a while to write a bit about major ones. It seems to me that you are more interested in where do post-Yugoslav states come from, so I will concentrate on that. Still, I'll list some major causes of the break up, and can expand on any or all if you want. So, major reasons, in no way in order of importance:
transfer of legitimation from socialist/communist one to national
economic issues, both prolonged crisis and the lack of transparency in relations between republics and federation (popularly the question of who is exploiting whom)
growing political and economic weight given to individual republics, gradually weakening the bonds between republics
ethnic tensions and developing animosity between nations (although, I consider ethnic hatred as much of a consequence as a cause)
loss of bearing in international relations after the end of Cold war, when Yugoslav position as socialist country between East and West lost all meaning
The list is by no means complete, but those are the causes I'd consider major.
As for the resulting post-Yugoslav states, most had more or less defined statehood even before Kingdom of Yugoslavia (1918 - 1941) was formed. Slovenia, part of Austrian lands in Austria-Hungary had well defined national culture, and compact, mostly ethnically homogeneous territory. Croatia was formally a separate kingdom withing Hungary, and quite a strong tradition of statehood. Serbia was an independent kingdom, formally from Berlin congress in 1878, but in practice even before that when it was part of Ottoman Empire, however from early 19th century mostly only on paper. Montenegro similarly was an independent kingdom.
Kingdom of Yugoslavia was broken apart in Second world war, but reconstituted, largely through successes of it own resistance movement as socialist federation. Internal borders of that federation were set up already in 1943, taking into account more historical than ethnic boundaries and defining the 6 republics I listed above. With some very minor corrections, those are the borders of todays states. All 6 were defined as sovereign states withing the federation, and when they proclaimed independence, they did so within those 1943 borders. Only exception is Kosovo, because although it was an autonomous region, was formally a part of Serbia.