When Einstein proposed his General Theory" of Relativity, he suggested some pretty strange ideas about space, time, and gravity.

How did scientists in 1919 show that Einstein's theory described the behavior of the real world and wasn't just a crazy hypothesis?

One of the takeaways of the General Theory of Relativity (GTR) was that the light can be curved because of the gravity of a massive object. Einstein had proposed the idea of space-time fabric. Every object having mass will create depression in this fabric. Heavier the object, bigger the depression. Thus when light will pass near a heavy object lets say our Sun, it will deflect. He also gave mathematical formula to calculate the deflection.

The same was proved during the Total Solar Eclipse of 29 May 1919. Two scientists named Arthur Eddington and Frank Dyson conducted an experiment. In this eclipse the Sun was to be in front of Hyades in Taurus constellation. They took the measurement of stars of Hyades visible during the eclipse and then compared them with the actual readings. The deflection was clearly visible and the amount of deflection was very close to the values predicted by General Theory of Relativity. Thus they proved the theory right.