Often through character crossovers. They put characters from both series in the same story. Like Harry and his friends could end up in Middle - earth, or the hobbits could find themselves at Hogwarts.
By melding the storylines. A fanfic might have the One Ring be a powerful dark magic object in the Harry Potter universe, and the characters from both stories have to work together to destroy it. This combines the central plot of 'Lord of the Rings' with the magical world of Harry Potter.
Character crossovers are a key way. Writers will bring characters from both universes into the same story. They might have Hermione meet Bella, and through their interactions, the two different worlds start to merge. The slash aspect can then be added by creating unique relationships between characters from the two series, like a budding romance between a wizard and a vampire. This not only combines the universes but also adds an interesting new dimension to the story.
They blend by combining characters. For instance, having Frodo in Westeros or Tyrion in Middle - earth. Also, the settings can be merged. The dark forests of Middle - earth can be made similar to the haunted woods in 'Game of Thrones'.
By using the characters' unique abilities. For example, Naruto's ability to quickly learn new skills could be used when he's in Middle - earth. He could learn some elvish magic or the ways of the Rohirrim. And the hobbits' stealth could be something that Naruto admires and tries to incorporate into his ninja tactics.
Many fanfictions also blend the storylines. The fight against the Empire in 'Star Wars Rebels' can be compared to the fight against Sauron in 'Lord of the Rings'. The rebels' struggle for freedom and justice can be seen as similar to the Fellowship's quest to destroy the One Ring. This way, the two universes are combined in a way that creates a whole new and exciting story.
The 'Harry Potter Fire Lord' fanfiction can combine the two universes by creating a portal or a magical accident that transports characters from one world to the other. For instance, a spell gone wrong in Hogwarts could send a character to the world of the Fire Lord.
One popular type might be those that explore the friendship between characters from both universes in a more in - depth way. For example, a fanfiction could focus on how Harry Potter and Frodo Baggins would interact if they were to meet, sharing their experiences of facing great evil.
In fanfiction, the magic in Harry Potter is more about spells and potions. Wizards learn specific incantations to produce magical effects. In Lord of the Rings, magic is more mysterious and often associated with the power of certain beings like Gandalf. So in a fem Harry Potter and Lord of the Rings crossover, the fem Harry might be confused by the more nebulous magic in Middle - earth at first.
One way is through power systems. The biotics in Mass Effect and the chakra in Naruto can be related. Maybe a character in a fanfiction discovers that biotics are a form of chakra or vice versa. Also, the different races in Mass Effect and the clans in Naruto can interact in terms of politics and alliances. For instance, the Uchiha clan could form an alliance with the Salarians based on their shared intelligence and strategic thinking. And the stories can also use the different settings, like having a battle take place on a Mass Effect planet but with Naruto - style combat techniques.
It might also combine them by setting the Tetris game in the Hogwarts castle. So, instead of a plain background, you have the Great Hall or the Gryffindor common room as the backdrop for the game. The sounds of the game could be replaced with magical noises like spells being cast or the flapping of a hippogriff's wings.
It can combine the two by having the characters cross over. For instance, Harry could be invited to MI6 to share his knowledge of dark magic as they face some sort of dark magical threat in the Muggle world.