The Sun started its life on the main sequence with approximately ten billion years worth of hydrogen fuel in its core. Consequently, an individual hydrogen nucleus there - a proton - can expect to live billions of years, and undergo zillions of close encounters with its fellows before winding up as part of a Helium nucleus. This means that the nuclear reactions (starting with tunneling through the coulomb barrier of another proton) are extremely infrequent and improbable.
This means that they can't be measured in the laboratory - no experiment could possibly attain sufficient luminosity to produce any interactions at the temperatures/velocities found in the Sun. Consequently, the nuclear reactions of the Sun and other stars mostly have to be modeled, extrapolated, and calculated. It's a remarkable triumph of theory that these calculations have been extremely successful, and that models of stars have passed test after test.