If Harry leaves to become a Dark Lord, his personality would have to change drastically. He would need to become more cold - hearted and power - hungry. He might start by making alliances with existing dark forces, like the remaining Death Eaters. He would then use his fame as 'The Boy Who Lived' to his advantage, convincing some that his new way is the right way. He could create his own brand of dark magic, mixing it with the things he learned at Hogwarts, and soon enough, the wizarding world would be in chaos as he rises to power.
In such a fanfiction, Harry might become a Dark Lord due to a tragic event. For example, if his friends are killed by the wrong side being misjudged as the enemy. This extreme grief and anger could lead him down the dark path. He would then use his knowledge and skills in a new, more sinister way. He could start by taking over Hogwarts, turning it into a place to teach dark magic instead of the traditional magic.
Well, one way could be that Harry feels betrayed by the wizarding world. Maybe he discovers some dark secrets about Dumbledore or the Ministry that make him lose faith in the so - called good side. So, he decides to embrace the dark arts. He starts learning from old, forbidden tomes and begins to gather followers who are also disillusioned with the current state of the wizarding world.