A common scenario is that Harry is made to scrub cauldrons. Snape would be hovering nearby, making sarcastic remarks about Harry's sloppiness. Another one could be that Harry has to organize Snape's Potions ingredients in alphabetical order while Snape quizzes him on their properties.
One interesting scenario could be that during detention, Snape makes Harry clean all the potion bottles in the dungeon while lecturing him about the importance of precision in potions. Harry, in turn, discovers an old, forgotten potion recipe among the bottles and Snape is grudgingly impressed.
One common detention scenario in Harry Potter fanfic could be having to clean the Forbidden Forest under the watchful eyes of Hagrid. The characters might encounter all sorts of magical creatures they've never seen before, like a rare breed of unicorn or a group of mischievous pixies. Another could be having to sort through a room full of old, cursed items in Filch's office, with the danger of accidentally triggering a curse.
One interesting scenario could be when the characters are in detention and they discover a hidden magical object. For example, in some fanfictions, Harry and his friends might find an old, enchanted diary during detention in the castle. This diary could hold secrets or be a portal to another time or place.
Well, Harry could be forced to clean the Potions classroom during detention. Snape might make him scrub every cauldron by hand while muttering about how clumsy Gryffindors are. Harry might accidentally spill a potion ingredient, which makes Snape even angrier and gives him more tasks to do, like sorting out all the potion ingredients in the store cupboard.
Well, in a detention with Snape in a Harry Potter fanfic, Harry might be forced to clean out the Potions storeroom. Snape could use this time to lecture Harry about his lack of respect for Potions as a subject. Maybe he would also drop some hints about Harry's father, James, which could be both infuriating and enlightening for Harry.
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.
One common theme is love. Snape's love for Lily is often explored in great detail, like how it shaped his actions and decisions. Another is redemption. Many fanfics focus on Snape's journey to redeem himself for his past mistakes. For example, his association with the Death Eaters in his youth. And there's also the theme of sacrifice. His ultimate sacrifice for Harry and the wizarding world is a big part of many fanfics.
Perhaps in the fanfiction, Snape assigns Harry to clean all the old potion vials in the storage room during detention. While doing so, Harry discovers an old diary that seems to hold secrets about Snape's past at Hogwarts, which then leads to a series of revelations and a change in their relationship.
Some fanfictions have the idea that while in detention, Harry and Snape are magically bound to work together on a special potion. This potion has the power to reveal hidden secrets. As they work on it, they start to share their own secrets, like Snape's unrequited love for Lily and Harry's fears about Voldemort. It's a really interesting way to develop their relationship.
One common scenario is Snape helping Harry with his Potions work. Since Snape is the Potions master, he might offer some extra guidance to Harry, which could be crucial for Harry's progress in school. Another scenario could be Snape protecting Harry from the bullying of other Slytherins. He might not do it in an obvious way, but still intervenes subtly.