Short answers, pulled from the story.
Arthur Eddington proposed in the year 1920 that massive spheres derived their energy from nuclear fusion converting hydrogen into helium. He based this hypothesis on precise measurements of atomic masses taken by F.W. Aston.
George Gamow solved a critical puzzle in 1928 regarding how nuclei could overcome electrostatic repulsion through quantum tunneling. His formula calculated the probability for two contiguous nuclei to approach each other closely enough for reaction despite physical barriers.
Hans Bethe published his landmark paper titled Energy Production in Stars during the year 1939. This work analyzed different possibilities for reactions fusing hydrogen into helium and identified the proton, proton chain reaction as dominant in stars with masses up to about one solar mass.
Margaret Burbidge, Geoffrey Burbidge, William Alfred Fowler and Fred Hoyle later unified research into what became the famous 1957 B2FH paper. Their work accounted for observed relative abundances of elements across the universe and described how advanced fusion stages synthesize elements from carbon to iron.
Each complete fusion cycle releases about 26.2 MeV of energy within lower-mass main-sequence stars like our Sun. A 10% rise in temperature increases energy production by this method by 46% because the reaction rate depends on temperature raised to approximately the fourth power.