The way these two universes are combined in fanfictions depends. It could be a shared threat that brings the characters together, or a character from one accidentally ending up in the other's world and causing chaos.
Well, in many fanfictions, they blend the universes by having the characters meet. For example, Percy might end up in the world of 'God of War' and have to deal with Kratos. This creates an interesting dynamic as their personalities and powers are quite different.
Some fanfictions blend the two universes by introducing elements of one into the other. For instance, the Death Note's rules might be applied in the Naruto universe. So a character in Naruto might get hold of a Death Note - like object with similar powers, and then the story explores how that changes the Naruto world's balance of power and relationships. It can also involve characters from Death Note trying to understand the ninja way of life in Naruto, which is full of loyalty, honor, and complex clan politics.
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'.
They blend elements by having Arrowverse characters use Infinity War - inspired tech or powers. For example, a character might get their hands on a version of the Power Stone and it gives them new abilities. Also, the settings can be a mix. You might see a battle take place in Star City but with the kind of epic scale and alien presence like in Infinity War.
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.
Writers often start by establishing a connection point. For example, a portal might be created that transports a Naruto character with the Sharingan to the Fairy Tail world. Then they use the unique aspects of each world. The Sharingan's abilities like predicting movements can be used in battles against Fairy Tail's magic.
In fanfiction, the two universes blend in multiple ways. The characters from Harry Potter can be put into Creepypasta - like situations. For instance, Harry might find himself in a situation where he has to face a entity that is not from the wizarding world but from a Creepypasta realm and has to use his magic in a new and untested way to survive. Also, the magic in Harry Potter can be warped to fit the spooky nature of Creepypasta. Spells could have unexpected and disturbing side - effects that are more in line with Creepypasta. The creatures in Harry Potter can also be made more menacing by borrowing elements from Creepypasta. For example, a Hippogriff could be made to look more like a nightmarish beast with Creepypasta - inspired features.
Well, one way is through food. Since food is a big part of both worlds. In Harry Potter, there are feasts and unique magical foods like Bertie Bott's Every Flavour Beans. Ramsay could be introduced to these and either be appalled or find ways to incorporate them into his cooking. For example, he could try to make a gourmet dish using the essence of Butterbeer.
The aesthetics blend quite well. RWBY has its vibrant color - coded characters and unique weapon designs. Transformers Prime has its sleek, mechanical look. In fanfictions, you might see Ruby's red cloak fluttering next to Optimus Prime's red and blue armor, creating a visually appealing contrast.
Writers blend the two universes by combining the magic systems. In Game of Thrones, we have magic like the wildfire and the warging ability. In Warcraft, there's arcane magic, druidic magic etc. A fanfic might have a character who can use both the warging ability from Game of Thrones and druidic magic from Warcraft, creating a really unique power combination. They also use the geography. Maybe a fanfic has a portal opening between the Seven Kingdoms and Azeroth, and then characters from both sides start exploring the other world. This allows for a lot of interesting interactions and conflicts.