This is connected to the idea of pan-slavism, an ideology that seeks the connection of a group of or even all slavic ethnicities in one nation.

First of all, it should be noted that what a nation state is is a complicated question. It is in most if not all cases rather a more or less arbitrary feeling of shared identity than actual ethnic unity. It is surprising how relatively few people actually spoke French as their mother language in the first French national assembly, but for example Occitan, Arpitan, Breton or German. About 2% of the Italians spoke what today is known as "Italian" when Italy was founded. Or, as the Sardinian Prime Ministre Massimo d'Azeglio put it: "We have made Italy. Now we must make Italians."

That being said, it might not be that hard to believe that two west slavic ethnicities with very similar languages like the Slovaks and Czechs decide to join forces. Actually, even subsuming all Slavs in what today is the Czech Republic under the term "Czechs" is questionable. The Czech term "Čechy" means nothing but "Bohemia", thus does not include Moravia and Austrian Silesia. The Slavic people in Czechoslovakia were actually four, the Bohemians (Czechs), Moravians, Silesians and Slovaks (and even more if you count Polish and East Slavic minorities). All of them felt (and still feel to some extend) similarities between each other, and from the point of view of someone in 1918, it was hardly possible to tell in which cases the similarities were enough to form one conjoint state. The common goal to get rid of the German and Hungarian rule and - which is different to 1992! - the ongoing fear of possible revisionism played their part and overshadowed differences.

There were never definite borders between the Austro-Hungarian ethnicities. Cities had mixed populations. It was impossible to form a nation state in the idealistic way intellectuals might have wanted it to be, at least not without doing what was done after the second world war - forcefully expelling millions of people of ethnic minorities and majorities. More than 3 millions of Germans, who were the second largest ethnic group with more people than the Slovaks, and several hundreds of thousands of Hungarians lived in Czechoslovakia. Many of them had important roles in the old K.u.K. administrations and were forced out of these jobs and replaced mainly by Czechs. This caused a lot of disaffection not only within the group of the old elites but also among the Slovaks who didn't profit as much as they, from their point of view, should definitely have.

The situation in Yugoslavia was similar, but worse. These peoples also share strong linguistic and cultural similarities, but there are still many differences and their identities are rather disintegrative.

- The Serbians are orthodox christians. In the middle ages, Serbia was a proud empire that even claimed the title of an emperor (tsar).

- The Bosnian christs are mostly catholic, but Bosnia once was a wealthy region. In the Ottoman Empire, only christians had to pay taxes, which made many Bosniaks convert to islam, while the poorer people around them did not have much to lose keeping their faith.

- The Croatians are catholic and historically (and geographically of course) much closer to western / central Europe. Croatia was in a union with Hungary since the 12th century.

So despite the similarities, these peoples are not culturally more or less the same and do not share much common history. And then, there are ethnic border territories like Krain / Slovenia, Kosovo and Macedonia that didn't contribute much to the Yugoslavian stability either. So, why did they even agree to form Yugoslavia?

Czechoslovakia had one war against Poland which annexed the tiny Zaolzie territory, but its existence was not threatened by anyone but the beaten Germans and Hungarians. Croatia and Slovenia however bordered Italy, a victorious, but highly frustrated power. Italy, or rather, a political movement in Italy, never considered their borders complete after their unification. Much of the eastern Adriatic coast was once ruled by the Venetian Republic; Italy considered these lands part of what they called "Italia Irredenta" - the "unliberated Italy". This basically forced the Austro-Hungarian successor states into Yugoslavia.

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I'd love to explain the situation after the Second World War as well, but I'll have to leave this to someone who knows more about it than I do.