Through shared adventures. For instance, if they get lost in a mysterious forest together. Ash would rely on Latios or Latias's ability to sense their surroundings and they would grow closer as they face the challenges of finding their way out. It could be as simple as Ash sharing his food with them during this time, showing kindness.
Well, in a Pokemon Latios x Latias fanfic, you can expect a story full of adventure. It might focus on their unique bond as siblings or their powers. Maybe it'll have them teaming up against a common enemy in the Pokemon world, like a powerful villainous team. It could also explore their relationship with trainers or other Pokemon in their environment.
Common themes in a Pokemon Latios x Latias fanfic include adventure, of course. They are powerful and fast Pokemon, so they can go on all sorts of exciting adventures. Another theme is mystery. Their psychic abilities and their somewhat elusive nature can be used to create a sense of mystery in the story. Also, the theme of friendship might be present, not just between them but also with other Pokemon they meet during their travels. For example, they might befriend a small group of Pokemon that are in trouble and help them out.
In some fanfictions, other legendary pokemon might also be important characters. For example, they could be involved in a plot where Latias, Latios and the other legendaries have to work together to save the pokemon world from a great threat. This would make all of them main characters in a sense as they are all crucial to the story.
There could be a fanfiction that focuses on the bond between latias and latios. Maybe one of them gets injured and the other has to go on a journey to find a special healing item. Along this journey, they learn more about themselves and their relationship, and also about the wider pokemon world.
One idea could be that Ash forms a special bond with Latios and Latias while on a journey in a new region. They help him discover a hidden power within himself. For example, Latios might be able to sense when Ash is about to make a wrong move in a battle and communicate it to him telepathically.
I don't think they are overly popular. Most Pokémon fans are interested in the positive aspects of the Pokémon relationships, like friendship and cooperation. Lemon fanfics, which often involve inappropriate content, are not something that the majority of the community would support or promote.
A good plot. It should have an interesting story that involves Ash, Latias, and Latios in a meaningful way. Maybe it could be about their adventures together, or a special bond that forms between them.
There are many out there. Some fanfics might explore a scenario where latios and latias have to overcome differences in their personalities to fully embrace their love. Maybe latios is more adventurous and latias is a bit more cautious, and the fanfic could show how they work through that. It could also be interesting to see how they interact with other Pokémon in the context of their love story, like how they might be protective of their relationship in front of other Pokémon or how other Pokémon might play matchmaker for them.
You can start by looking on fanfiction websites like FanFiction.net or Archive of Our Own. They have a large collection of fanfics related to various characters, including Ash, Latias, and Latios. Just use the search function on these sites and type in the relevant tags.