Two atoms of ionized hydrogen (H+, a single proton each) are moving so quickly that they overcome their electromagnetic (coulomb) repulsion and slam into each other. This forces the weak nuclear force to convert one of the protons' quarks to decay, switching that proton to a neutron; this forms deuterium. In this process of proton transmutation, one positron and one neutrino are shot outwards. This is an endothermic reaction, meaning it actually takes energy to occur. On average, these particles may wait for over several hundred million years before this occurs.
That positron doesn't last long as it soon finds one of Helios's abundant unbound electrons, annihilating both positron and electron and shooting forth two gamma ray photons.
One deuterium atom smashes into another ionized hydrogen atom. They fuse, releasing a single gamma ray photon and we now have a helium atom shy of one neutron, known as 3He - a light isotope of helium.
Two of the 3He atoms collide, sending two of the protons back out into the core, creating the normal helium atom with two protons and two neutrons.
This only occurs 86% of the time in star of Helios' mass. Every now and then, the helium isotope will collide with a normal helium atom instead, and these will fuse to make beryllium, which may then grab an electron to make lithium which will then collide with ionized hydrogen to make two normal helium atoms instead of just one. This becomes the most common reaction at temperatures of 14 to 23 million kelvins .
Or even more occasionally, that beryllium atom may collide with a hydrogen ion to make boron, which then breaks down into a heavy beryllium isotope which then breaks down into two normal helium atoms. This becomes the most common reaction only at temperatures exceeding 23 million kelvins .
The math also predicts an extremely rare instance of the helium isotope colliding with ionized hydrogen to directly make normal helium. This has never been observed, however.
In stars of greater mass (and thusly greater temperature) a different reaction becomes prevalent. The proton-proton reaction still occurs, but a process known as the CNO Cycle (so named for the involved parties: carbon, nitrogen and oxygen) becomes the dominant force in hydrogen's conversion to helium.
Many stars contain some amount of carbon, nitrogen and oxygen in ionic form. If these elements are present, the temperature is greater than 16 million Kelvins and the star's mass is at least 10% greater than Helios, the CNO cycle becomes predominant.
It often begins with carbon-12.
Ionized carbon-12 collides with ionized hydrogen to emit a gamma ray, and briefly exist as nitrogen-13.
This nitrogen-13 form is unstable and quickly falls apart through beta plus decay. To balance the instability, the weak force uses energy to change a proton into a neutron (as in the proton-proton chain reaction), emitting a positron and neutrino.
Now stable as carbon-13, another H+ collision occurs and another gamma ray is emitted.
Still stable as nitrogen-14, a third collision with H+ yields a third gamma ray and oxygen-15.
Once again unstable, oxygen-15 takes some more energy to beta plus decay, and settle into nitrogen-15 instead. The positron is quickly annihilated, as always, and the neutrino escapes to travel the universe.
When this nitrogen-15 hits H+, it becomes unstable and releases an alpha particle instead of a gamma ray. This alpha particle is a complete helium nucleus, and this leaves behind carbon-12, the same ion the process began with.
This is a catalytic conversion due the necessity of carbon-12 to begin the process, but the end result leaving behind the very same.
Being a catalytic cycle, this "loop" can be repeated several times with minimal amounts of carbon, nitrogen, and oxygen and large amounts of hydrogen.
There are two other minor branches in which the alpha particle is not released until later, the CNO II branch, and the OF branch. They are even rarer except in much heavier stars.