How can a broken finger heal?

Immobilize. In an uncomplicated finger fracture, healing only requires immobilizing the fingerr (with a finger splint) for 4-6 weeks.
Boney union 8-14wks. A broken finger takes time for the bones to mend which is typically slower than other parts of the body due to the small bone size, blood supply and movement and instability. Whereas many bones form a union within 6-8 weeks, the finger bones may take anywhere from 8-14 weeks.