Often, in the fanfic, it could be that Harry is injured during a Quidditch match. Snape, despite his dislike for Harry in some ways, realizes the importance of Harry to the wizarding world and heals him. There could also be a situation where Harry is affected by some dark magic in the Forbidden Forest. Snape, who has a deep understanding of dark magic, is the only one who can counter it and heal Harry. It might also happen that Harry is suffering from the after - effects of using powerful magic, and Snape uses his own unique magic to heal Harry's drained energy.
One common scenario is after a battle. Harry is injured, and Snape, despite their differences, steps in to heal him. Maybe it's a fight against the Death Eaters where Harry is seriously wounded, and Snape realizes he has to put aside their enmity for the greater good.
In some fanfictions, Snape might use his advanced knowledge of potions to brew a special healing elixir for Harry. He could also use his magic skills, like a complex spell specifically designed to mend Harry's wounds, whether they are physical or emotional.
One great 'Harry heals Snape' fanfiction could be 'The Healing Bond' where Harry discovers a new spell that can reverse the dark magic effects on Snape. It's a very detailed story that delves into their complex relationship.
One common plot device is the revelation of Snape's hidden motives. As he heals Harry, we might discover that his actions are not just out of duty but also out of a long - held, unspoken love or loyalty. Another is the use of rare and dangerous ingredients in the potions he makes for Harry's healing.
Snape could also use his magical abilities in a more emotional sense. He might share his own past traumas with Harry, creating a bond of understanding that starts to heal Harry's broken spirit. By being vulnerable himself, he shows Harry that it's possible to move past pain.
The healing might make Harry feel indebted to Snape. This could change their relationship from one of animosity to one where Harry is more open to Snape. Snape, on the other hand, might still be his usual guarded self, but the act of healing could create a crack in the wall he has built between them. Harry might begin to question his previous assumptions about Snape and be more willing to cooperate with him in certain situations.
You can try fanfiction.net. It has a large collection of Harry Potter fanfictions and there are likely to be several 'Harry heals Snape' ones there.
In some fanfictions, Snape might use his advanced knowledge of potions to create a special concoction to heal Harry. He could draw on his skills in Herbology as well to find rare ingredients for the potion.
One common theme is redemption. Snape has had a rather complex and often villain - like portrayal in the original series, and in these fanfictions, Hermione's healing of him can be seen as a way to redeem him, both physically and emotionally.
One reason could be the loss of a loved one. Maybe Harry has lost Ron or Hermione in a battle, and this has left him in a state of despair.