Other people are still posting so I'll throw some things into the pot.
The interbellum years for Central and Eastern Europe are divided into three main parts:
1. 1918-1922 (The Immediate Afterwar Years)
2. 1922-1929 (The Middle Years)
3. 1929-1939 (The Ugly Years - [my term])
1. The Immediate Post-War Years
As the World War wound down the empires all began to collapse; Austria-Hungary in October 1918, Germany in November, and the Ottoman empire by late November. The Russian empire had imploded the previous Spring, in March 1917. The end of the war and the end of the empires brought...more wars. Churchill made the famous remark that after the march of the giants ended, the march of the pygmies began - the little countries and their little wars. Russia was plunged into Civil War from the revolutions in March and November 1917, Poland fought against Ukrainians, Lithuanians, Czechs, Germans and Soviets; the Czechs fought the Hungarians and Poles, the Hungarians fought Serbs, Czechs, and Romanians; the Romanians fought Hungarians, Ukrainians and Serbs; the Bulgars fought Greeks, Romanians and Turks; the Greeks fought Turks, Bulgars and Albanians; etc. etc. etc. You get the idea.
Revolutions also were the rage. Hungary slid into a communist revolution after the Allies refused to negotiate with the Democratically-elected government, bringing Bela Kun and the Tanácsköztársaság ("Republic of Councils") to power for 133 days before the French asked the Romanians to invade and overthrow it. Bavaria also became, briefly in 1919, a communist republic.
After the communist government fell in Budapest, Karl of the House of Habsburg tried twice to regain his throne in Hungary, both unsuccessfully. Miklos (Nicholas) Horthy, an old admiral in the Austro-Hungarian navy, took over as virtual dictator and he would rule Hungary until 1944. Horthy became officially regent, so Hungary throughout the interbellum years was a kingdom without a king, led by an admiral without a navy.
Democracy was the fashion though - most countries, new and old, attempted to establish at least some sort of Democratic government. Poland, Czechoslovakia, Lithuania, Latvia, Estonia, Ukraine, Hungary, the Kingdom of Serbs, Croats and Slovenes (which would later in 1929 be re-named simply "Yugoslavia"), Bulgaria, Romania, Greece; all started out with the best of political intentions.
2. The Middle Years:
These years brought stability to the region, though not necessarily prosperity. The civil wars ended, the territory wars ended, borders stabilized, as did hatreds. Democracies in this period all stumbled or fell, one by one. Some did so softly; Poland and Hungary each ended up with benevolent dictators who allowed parliamentary elections and opposition, but only so far. The 3 Baltic states slid into a fascist-style dictatorship. Greece became ultra-nationalistic after its defeat in the 1918-1922 Anatolian wars with Turkey, and Croat nationalists began to attack the Serb-dominated kingdom. Czechoslovakia was the only state in all Central Europe (including Germany!) to remain a fully-functional democracy right up until Nazi troops dismantled the country in 1938.
The Middle Years were fairly good years, at least compared to the 1930s. Warsaw, Prague and Budapest all had very active cultural lives with famous cabaret acts and great night clubs.
The problem was that everyone wanted everyone else's real estate. Europe in the interbellum years was divided into two camps: Those who wanted to keep the Versailles Treaty borders and Those who wanted to change them. Group A. consisted of France, Britain, Poland, Czechoslovakia, Romania, Yugoslavia, the Low Countries, etc. Group B. was led by Germany, and consisted of Hungary, Italy, Bulgaria, and possibly Austria. Some countries - Greece - were on the fence. In other words, Group A. was countries who'd gained land after the war and wanted to keep it; Group B. was countries who'd either lost land or didn't get all the land they wanted. This is complicated by a problem in Europe that is universal; that virtually any city or region has belonged to several cultures or nations at different times. For instance, Alsace-Lorraine of France was part of the old Alsatz and Lotharingia region of the Germanies, and as late as the 18th century Strasbourg's population was German. So countries were trying to conquer all the regions that had ever been apart of their cultures or histories. Even when the armies weren't marching, these countries refused to trade with each other - Hungary in 1929 was trading far more with the United States far overseas than with all of her neighbors combined. This made it easy for Germany in the 1930s to enter the region economically and make all the small countries dependent on the Reich.
The French had attempted to set up an anti-German alliance in the East in the early 1920s, called the Little Entente (Entente petit). This consisted of Czechoslovakia, Romania and Yugoslavia. However, this alliance was useless for many reasons. First, it failed to include the country in the region with the largest population and army (next to Germany), Poland, because the Czechs hated the Poles and because everyone feared the Poles would start a war with Soviet Russia or Germany and drag them all in. Secondly, the three allies in the region were more interested in making sure Hungary didn't try to take back any of the land they all swiped from the Hungarians, so while the French hoped for an anti-German alliance, they ended up with an anti-Hungarian alliance. This drove the Hungarians closer to both the Italians and the Germans. Finally, the reality was that the French believed themselves to be a great power, but after the war they were unable to support any major military efforts in Europe and their post-war influence melted away. When Hitler marched into Czechoslovakia in 1938, not only did the West do nothing but Czechoslovakia's fellow Little Entente allies didn't lift a finger either. In fact, they fell over themselves to sign new treaties with Hitler.
3. The End Years:
The Western countries signed two treaties with Hitler's Germany in the 1930s, Rapallo and Locarno, that guaranteed Germany's western borders but not the eastern borders - which Hitler thought meant the West was saying he could do what he wanted in the East. The Great Depression had economically devasted all the countries of the region, and ultra-nationalists came to power in most countries. You know the story here - German re-armament, militarization of the Saarland and the Rhein, and expansion of the German economy to the economically-wasted East.
It was only a matter of time before war broke out again....
Write me if you want specific names of leaders, etc..