How do nuclear fusion reactions start?
When the gravitational force of a proto-star's mass is sufficient to fuse hydrogen nuclei.
Fusion is the combining of atomic nuclei into larger atoms. The process releases huge amounts of energy. We achieve it currently only atomic bombs that use a fission nuclear reaction driver and at a very small and temporary scale with laser implosion of tritium.
In stars the driving force is the gravitational force of the stars mass. Thus, a star's nuclear fusion processes may be said to “start” when the accreting mass is sufficiently dense to force small nuclei together.