A quick Google search is not exactly deep scholarship, but should do for my purposes.
After WWI many new nations appeared in Central Europe as the German and Austro-Hungarian empires were dissolved. Some also appeared as break-aways from the Russian Empire. These countries were, in the main, extremely nationalistic, tended to be militaristic and despotic, and were virulently anti-Communist (and often virulently anti-Semitic). Ironically, Czechoslovakia was the one country that was almost none of these things.
Their internal politics was difficult before the Great Depression, but hopeless afterwards. The rise of the Nazis in Germany influenced many of these nations to fashion political parties on the Nazi model. In Hungary you had the Cross Arrow Party and in Romania something called the National Socialist Romania Party. Romania also had a large number of other right-wing parties, most prominent of which was the Iron Guard.
While there was no great love for Germany, there was a desire to emulate the economic success of the Nazis in pulling Germany out of the Great Depression. There was also a desire to ensure that they did not fall victim to the ambitions of Soviet leader Stalin.
When the War began German successes were amazing, from their point of view. While Britain was probably far better off in the fall of 1940 than either Goebbels or Joe Kennedy said they were the hard truth was that they had been defeated in detail in France. That the British had won the Battle of Britain did not mean they were in the clear (any more than the U.S. victory at Midway ended the Japanese threat). From the perspective of anti-Communist leaders in Central Europe it would have been clear that the Germans were the coming power. It was only a matter of time.
German success in Russia in the fall of 1941 would have further convinced the Central European states that Germany was their best hope. The Werhmacht had easily defeated the Red Army, inflicting catastrophic casualties. This would have been further motivation to engage in active military operations in hope of not only permanently removing the Russian threat, but maybe even obtaining additional territory.
So they cast their lot with the Axis. With the aid of 20/20 hindsight this was a dramatically bad decision. But from the perspective of the time it made good sense.