The process in which hydrogen nuclei combine with each other to form helium and other heavier elements is called Nuclear Fusion.
Nuclear Fusion happens when the repulsion between the two nuclei is overcome by the Strong Interaction Force, spending and releasing high amounts of energy.
The two nuclei need to be close enough for Nuclear Fusion to happen, and the energy needed to achieve that is given by the extremely hot temperatures that exist within stars (about 15 000 000 Kelvin). That's why this kind of reactions are common in stars.
