In some fanfictions, Hermione is able to do wandless magic through intense study and practice of ancient magical theories. She might have delved deep into books that are long forgotten by most wizards, and from there, she discovers the secrets of channeling magic without a wand. For example, she could have found out about the natural energy flows within the wizarding world and learned how to tap into them using just her willpower and magical knowledge.
You can start by looking on fanfiction platforms like Archive of Our Own (AO3). Just search for 'Hermione does wandless magic' in the search bar, and it should bring up relevant stories. There are also some other smaller fanfiction websites, but AO3 usually has a large collection.
There's also a story called 'Hermione's New Magic' on Fanfiction.net. In this one, Hermione starts doing wandless magic as a result of an accident in the library, and it leads to all sorts of interesting plot developments as she tries to master this new skill. The author does a great job of showing Hermione's character growth throughout the story. It's quite long and detailed, which makes it really enjoyable.
In some fanfictions, Harry Potter might develop his wandless magic skills through intense mental training. He could practice focusing his magic without the aid of a wand, much like how he learned to control his Patronus. By visualizing the desired outcome clearly in his mind and concentrating his magical energy, he gradually becomes proficient at wandless magic.
One of the most impressive feats could be large - scale teleportation. In some fanfictions, Harry Potter manages to transport himself and others over long distances without a wand, which is extremely difficult magic even with a wand. Another could be instantaneously conjuring complex magical shields to protect against powerful dark spells, all wandlessly.
One interesting fanfiction is 'Hermione's Wandless Adventure'. In this, Hermione starts doing wandless magic after a strange encounter in the Forbidden Forest. The story follows her as she tries to understand this new ability and how it changes her relationship with her friends and the wizarding world. It's really cool as it shows her in a whole new light, not just as the book - smart girl but as a powerful magic - wielder without a wand.
In certain fanfic concepts, it might be due to some ancient magic within him that he wasn't aware of. Maybe he has a special heritage or a connection to a long - lost magic that surfaces spontaneously, leading to his discovery of wandless magic. This could be related to his parents or some other mysterious aspect of his family history.
There's also 'Wandless Ways of Harry Potter'. This fanfic delves deep into the concept of wandless magic. It has Harry learning from an ancient wizard who has mastered the art. The story is full of interesting spells and magical theories that are unique to wandless magic, making it really engaging.
In some fanfictions, Harry Potter uses his strong emotions and willpower to perform wandless magic. For example, in times of extreme danger or when he has a very intense desire to protect someone, he can tap into his inner magic without the need for a wand.
Overcoming limitations is also a theme. Since wandless magic is not the norm in the wizarding world as presented in the original books, Harry has to break through the traditional thinking. He has to deal with the doubts of others and his own insecurities. In some fanfics, he even has to face opposition from the Ministry of Magic who are wary of this unregulated form of magic.