With bright smiles, the two of them started walking toward a shining future.

Literal

Bright smiling-face [with-で] two-people [topic-は] sparkling future [object-を] walk-start [explanatory-んだ].

Fairy-tale or romance-story ending. 光り輝く ('to shine, sparkle, be radiant') is a compound of 光る ('to shine') + 輝く ('to shine brightly'). The reduplication gives a heightened poetic effect. 歩み始める uses the compound verb ending ~始める attached to the literary 歩む ('to walk, progress') — more poetic than 歩く. Textbook happy-ending narration.